LIBRARY OF CONGRESS. 




Chap. Copyright No. 

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The Great Telescope of the Lick Observatory. Aperture, 36 inches; Length, 57 feet. 






LESSONS m ASTRONOMY 



Including Ueanogbaphy 



A BEIEF INTRODUOTOEY COXJESE 



WITHOUT MATHEMATICS 




CHARLES A. YOUNG, Ph.D., LL.D. 

Professor of Astronomy in the College of New Jersey (Princeton) 

Author of a " General Astronomy for Colleges and Scientific 

Schools," and of "Elements of Astronomy." 







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Boston, U.S.A., and London 
GINN AND COMPANY, PUBLISHERS 

1896- 



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Entered at Stationers* Hall, 



Copyright, 1895, 
By CHARLES A. YOUNG. 



All Rights Reseryed. 



Typography by J. S. Cushing & Co., Boston. U.S.A. 



Presswork by Ginn & Co., Boston, U.S.A. 



PBEFACE. 



This volume has been prepared to meet the want of certain 
classes of schools which find the author's " Elements of 
Astronomy " rather too extended and mathematical to suit 
their course and pupils. It is based upon the Elements, but 
with many condensations, simplifications, and changes of 
arrangement : everything has been carefully worked over and 
rewritten, in order to adapt it to those whose mathematical 
attainments are not sufficient to enable them to use the larger 
work to advantage. 

Of course, such pupils cannot gain the same insight into the 
mechanism of the heavens as those who take up the subject 
at a more advanced stage in their education. They must often 
be contented with the bare statement of a fact without any 
explanation of the manner in which its truth is established, 
and thus will necessarily miss much that is most valuable in 
the discipline to be derived from the study of Astronomy. 

But enough remains — surely there is no other science 
which, apart from all questions of How or Why, supplies so 
much to widen the student's range of thought, and to make 
him comprehend his place in the infinite universe. 

The most important change in the arrangement of the book 
has been in bringing the Uranography or " constellation-trac- 
ing," into the body of the text, and placing it near the begin- 
ning; a change in harmony with the accepted principle that 
those whose minds are not mature succeed best in the study 
of a new subject by beginning with what is concrete, and 
appeals to the senses, rather than with the abstract principles. 



VI PREFACE. 

It has b^en thought well also to add brief notes on the legen- 
dary mythology of the constellations for the benefit of such 
pupils as are not likely to become familiar with it in the 
study of classical literature. 

In the preparation of the book .great pains have been taken 
not to sacrifice accuracy and truth to compactness ; and no less 
to bring everything thoroughly down to date. # # # # * 

The Appendix contains in its first chapter descriptions of 
tka.niost us&d .astronomical ^^^ instruments, and where time 
permits.,. might profitably .be brought into the course. The 
second chapter of the Appendix is designed only for the use 
of teachers and the niorg.. advanced pupils Arts. 431-434, 
however, explaining how :the sun's distance may be found in 
the simplest way, might well be. read by ., all. 

My warmest thanks are due to my friend and assistant, Mr. 
Taylor Beed, who has gone over all the proofs of the book, 
and has given me many valuable suggestions. 

PREFACE TO THE EDITION OF 1895. 

Since the fir^t publication of this work the progress of 
astronomy has been so rapid that in order to keep abreast of 
the times it has become necessary to give the book a thorough 
revision. This has been done : numerous minor changes and 
corrections have been made, some articles have been re- 
written, and others added. At the same time the alterations 
have been so managed that they will cause no serious incon- 
venience in using the older editions in connection with the 
new one in class-room work. 

It is hoped that, so far as its scope permits, the book now 
presents a satisfactory summary of the existing state of the 
science. 

August, 1895. 



CONTENTS. 



PAGES 

CHAPTER I. — Introduction : Fundamental Notions and Defi- 
nitions. — The Celestial Sphere and its Circles. — Altitude 
and Azimuth. — Right Ascension and Declination. — Celestial 
LatitudeandLongitude . . . . . . . . 1-16 

CHAPTER II. — Ukanography : Globes and Star-maps. — Star . 
Magnitudes. — Names and Designations of Stars. — The Con- 
stellations in Detail 17-54 

CHAPTER III.— Fundamental Problems : Latitude and the 
Aspect of the Celestial Sphere. — Time, Longitude, and the 
Place of a Heavenly Body . . . <: ; . ; . :;. .^$5-67 

CHAPTER IY. — The Earth: Its. .Form and Dimensions ; its 
Rotation, Mass, and Density; its Orbital Motion and the 
Seasons. — Precession.— The Year and the Calendar . v 68-90 

CHAPTER V.~ The Moon: Her Orbital Motion and the Month. : 

— Distance, Dimensions, Mass, Density,'' and Force of Grav- : ! ; s 
-' ity. — Rotation and Librations. ■*— Phases. — Light and Heat. 

— Physical Condition. — Telescopic Aspect and Surface . . 91-110 

CHAPTER VI. — The Sun: Its Distance, Dimensions,; Mass, and 
Density. — Its Rotation, Surface, and Spots. — The ' Spectro. 
scope and the Solar Spectrum ; the Chemical Constitution of 
the Sun. — The Chromosphere and Prominences. — The Cor- 
ona. —The Sun's Light. — Measurement and Intensity of the 
Sun's Heat. — Theory of its Maintenance, and Speculations 
regarding the Age and Duration of the Sun . . . 11 1-143 



V1U CONTENTS. 



CHAPTER VII. — Eclipses and the Tides : Form and Dimen- 
sions of Shadows. — Eclipses of the Moon. — Solar Eclipses, 
Total, Annular, and Partial. — Number of Eclipses in a Year. 

— Recurrence of Eclipses, and the Saros. — Occupations. — 

The Tides 144-158 

CHAPTER VIII. — The Planetary System : The Planets in 
General. — Their Number, Classification, and Arrangement. — 
Bode's Law. — Orbits of the Planets. — Kepler's Laws and 
Gravitation. — The Apparent Motions of the Planets and the 
Systems of Ptolemy and Copernicus. — Determination of the 
Planets' Diameters, Masses, etc. — Herschel's Illustration of 
the System. — Description of Individual Planets : the ' Ter- 
restrial ' Planets, Mercury, Venus, and Mars . . . 159-189 

CHAPTER IX. — Planets (continued) : The Asteroids. — Intra- 
Mercurian Planets and the Zodiacal Light. — The Major Plan- 
ets, Jupiter, Saturn, Uranus, and Neptune. — Ultra-Neptunian 
Planet 190-212 

CHAPTER X. — Comets and Meteors: Comets, their Num- 
ber, Designation, and Orbits ; their Constituent Parts and 
Appearance ; their Spectra, Physical Constitution, and Proba- 
ble Origin ; Remarkable Comets ; Photography of Comets ; 
Aerolites, their Fall and Characteristics ; Shooting Stars and 
Meteoric Showers ; Connection between Meteors and Comets 213-249 

CHAPTER XL — The Stars : Their Nature, Number, and Des- 
ignation. — Star Catalogues and Charts. — Their Proper 
Motions, and the Motion of the Sun in Space. — Stellar Par- 
allax. — Star Magnitudes and Photometry. — Variable Stars. 

— Stellar Spectra . . .' 250-274 

CHAPTER XII. —The Stars (continued) : Double and Multi- 
ple Stars ; Clusters and Nebulae ; the Milky Way, and Distri- 
bution of Stars in Space ; the Stellar Universe. — Cosmogony 
and the Nebular Hypothesis 275-301 






CONTENTS. IX 



APPENDIX. 

PAGES 

CHAPTER XIII. — Astronomical Instruments: The Telescope, 
Simple Refracting, Achromatic, and Reflecting. — The Equa- 
torial. — The Filar Micrometer. — The Transit Instrument. — 
The Clock and the Chronograph. — The Meridian Circle. — 
The Sextant 302-320 

CHAPTER XIV. (for the most part supplementary to Arti- 
cles in the Text). — Hour- angle and Time. — Twilight. — 
Determination of Latitude. — Place of a Ship at Sea. — Find- 
ing the Form of the Earth's Orbit. — The Ellipse. — Illustra- 
tions of Kepler's l Harmonic • Law. — The Equation of Light, 
and the Sun's Distance determined by it. — Aberration of 
Light. — De l'lsle's Method of getting the Sun's Parallax from 
a Transit of Venus. — The Parabola and the Conic Sections. 
— Determination of Stellar Parallax .... 321-339 

QUESTIONS FOR REVIEW ....... 340 

TABLES OF ASTRONOMICAL DATA: 

I. Astronomical Constants 347 

II. The Principal Elements of the Solar System . . . 348 

III. The Satellites of the Solar System 349 

IV. The Principal Variable Stars 350 

V. The Best Determined Stellar Parallaxes .... 351 

VI. The Greek Alphabet and Miscellaneous Symbols . . 352 

INDEX 353 

STAR-MAPS 367 



CHAPTER I. 

INTRODUCTION. — FUNDAMENTAL NOTIONS AND DEFINI- 
TIONS. — THE CELESTIAL SPHERE AND ITS CIRCLES. 
— ALTITUDE AND AZIMUTH. — RIGHT ASCENSION AND 
DECLINATION. — CELESTIAL LATITUDE AND LONGITUDE. 

1. Astronomy 1 is the science which deals with the heavenly 
bodies. 

As it is the oldest of the sciences, so also it is one of the 
most perfect, and in certain aspects the noblest, as being the 
most " unselfish " of them all. And yet, although not bearing 
so directly upon the material interests of life as the more 
modern sciences of Physics and Chemistry, it is of high utility. 
By means of Astronomy the latitudes and longitudes of places 
upon. the earth's surface are determined, and by such determi- 
nations alone is it possible to conduct vessels upon the sea. 
Moreover, all the operations of surveying upon a large scale, 
such as the determination of the boundaries of countries, de- 
pend more or less upon astronomical observations. The same 
is true of operations which, like the railway service, require 
an accurate knowledge and observance of time ;. for the funda- 
mental timekeeper is the diurnal revolution of the heavens, as 
determined by the astronomer's transit-instrument. 

In ancient times the science was supposed to have a still higher 
utility. It was believed that human affairs of every kind, the welfare 
of nations, and the life history of individuals alike, were controlled, 

1 The term is derived from two Greek words: astron, a star, and 
nomos, a law. 

1 



2 THE HEAVENLY BODIES. [§ 1 

or at least prefigured, by the motions of the stars and planets ; so 
that from the study of the heavens it ought to be possible to predict 
futurity. This belief is embodied in the pseudo-science of " Astrol- 
ogy," long since shown to be a baseless delusion though it still 
retains a hold upon the credulous. 

2. The heavenly bodies include, first, the solar system, — 
that is, the sun and the planets which revolve around it, with 
their attendant satellites ; second, the comets and the meteors, 
which also revolve around the sun, but are bodies of a very 
different nature from the planets, and move in different kinds 
of orbits ; and, thirdly, the stars and nebulae. The earth on 
which we live is one of the planets, and the moon is the earth's 
satellite. The stars which we see are bodies of the same kind 
as the sun, shining like him with fiery heat, while the planets 
and the satellites are dark and cool like the earth, and visible 
to us only by the sunlight they reflect. As for the comets and 
nebulae, they appear to be mere clouds, composed of heated gas 
or swarms of little particles of more solid substances, perhaps 
not very hot, but luminous from some cause or other. The 
telescope reveals millions of stars invisible to the naked eye, 
and there are others, possibly thousands of them, that do not 
shine, but manifest their existence by affecting the motions 
of their neighbors. 

3. As we look off from the earth at night, the stars appear 
to be all around us, like glittering points fastened to the inside 
of a huge hollow globe. Really they are at very different dis- 
stances, all enormous as compared with any distances with 
which geography makes us familiar. Even the moon is eighty 
times as far away as New York from Liverpool, and the sun 
is nearly four hundred times as distant as the moon, and the 
nearest of the stars is more than two hundred thousand times 
as distant as the sun ; as to the remoter stars, some of them 
are certainly thousands of times as far away as the nearer 
ones, — so far that light itself is thousands of years in coming 



§ 31 THE HEAVENLY BODIES. 3 

to us from thein. These are facts which, are certain, not mere 
guesses or beliefs. 

Then, too, as to their motions. Although the heavenly bodies 
seem to us for the most part to be at rest, except as the earth's 
rotation makes them appear to rise and set, yet really they are 
all moving, and with a swiftness of which we can form no con- 
ception. A cannon-ball is a snail to the slowest of them. The 
earth itself in its revolution around the sun is flying eighteen 
and a half miles in a second, which is more than thirty times as 
fast as the swiftest rifle bullet. We fail to perceive the motion 
simply because it is so smooth and so unresisted. The space 
outside our air contains nothing that can sensibly obstruct 
either sight or motion. 

4. But this knowledge as to the real distance and motions 
of the heavenly bodies was gained only after long centuries of 
study. If we go out to look at the stars some moonless night 
we find them apparently sprinkled over the dome of the sky 
in groups or constellations, which are still substantially the 
same as in the days of the earliest astronomers. At first these 
constellations were figures of animals and other objects, and 
many celestial globes and maps still bear grotesque pictures 
representing them. At present, however, a constellation is 
only a certain region of the sky, limited by imaginary lines 
which divide it from the neighboring constellations, just as 
countries are divided in geography. As to the exact boun- 
daries of these constellations, and even their number, there is 
no precise agreement among astronomers. Forty-eight of them 
have come down to us from the time of Ptolemy, 1 and even in 
his day many of them were already ancient. 

About twenty more, which have been proposed by more 
recent astronomers, are now recognized, besides a considerable 
number which have been abandoned. 

1 Ptolemy, the greatest astronomer of antiquity, flourished at Alexan- 
dria about 130 a.d. 



4 UR ANOGKAPHY. [§ 6 

5. TJranography, or Description of the Visible Heavens.— 

The study of the constellations, or the apparent arrangement 
of the stars in the sky, is called Uranography. 1 It is not an 
essential ■ p&it of Astronomy, but it is an easy and pleasant 
study; and in becoming familiar with the constellations and 
their principal stars, the pupil will learn more readily and 
thoroughly than in any other way the most important facts in 
relation to the apparent motions of the heavenly bodies, and 
the principal points and circles of the celestial sphere. For 
this reason the teacher is urged to take the earliest oppor- 
tunity to have his pupils trace such of the constellations as 
happen to be visible in the evening sky when they begin the 
study of Astronomy. 

6. The Celestial Sphere. 2 — The sky appears like a hollow 
vault, to which the stars seem to be attached, like specks of 
gilding upon the inner surface of a dome. We cannot judge 
of the distance of this surface from the eye, further than to 
perceive that it must be very far away. It is therefore natural 
and extremely convenient to regard the distance of the sky as 
everywhere the same and unlimited. The { celestial sphere? as 
it is called, is conceived of as so enormous that the whole world 
of stars and planets lies in its centre like a few grains of sand 
in the middle of the dome of the Capitol. Its diameter is 
assumed to be immeasurably greater than any actual distance 
known, and greater than any quantity assignable. In technical 
language it is taken as mathematically infinite. 

Since the celestial sphere is thus infinite, any two parallel 
lines drawn from distant points on the surface of the earth, or 
even from points as distant as the earth and the sun, will seem 
to meet at one point on the surface of the sphere. If the two 



1 From the Greek, ouranos (heavens), and graphe (description). 

2 The study of the celestial sphere and its circles is greatly facilitated 
by the use -of a globe, or armillary sphere. Without some such -appa- 
ratus it is not easy for a young person to get clear ideas upon the subject. 



§6] 



APPARENT PLACE OF A HEAVENLY BODY. 



lines were anywhere a million miles apart, for instance, they 
will, of course, .still be a million miles apart when they reach 
the surface of the sphere ; but at an infinite distance even a 
million miles is a mere nothing, so that the two lines make 
apparently but a single point 1 where they pierce the sphere. 

7. The Apparent Place of a Heavenly Body. — This is sim- 
ply the point where a line drawn from the observer through 
the body in question, continued 
outward, pierces the celestial 
sphere. It depends solely upon 
the direction of the body, and 
is in no way affected by its dis- 
tance from us. Thus, in Fig. 1, 
A, B, C, etc., are the apparent 
places of a, 6, c, etc., the observ- 
er being at 0. Objects that are 
nearly in line with each other, 
as h, ?, k, will appear close to- 
gether. The moon, for instance, 
often looks to us very near a star, which is really of course at 
ah enormous distance beyond her. 

8. Angular Measurement. — It is clear that we cannot prop- 
erly describe the apparent distance of two points upon the 
celestial sphere from each other by feet or inches. To say 
that two stars are about five feet apart, for instance, — and it 
is not very uncommon to hear such an expression, — means 
nothing unless we know how far from the eye the five-foot 
measure is to be held. The proper units for expressing appar- 
ent distance in the sky are those of angle, viz. : degrees (°), 
minutes ( f ), and seconds (") ; the circumference of a circle 
being divided into 360 degrees, each degree into 60 minutes, 
and each minute into 60 seconds. Thus, the Great Bear's tail, 




Fig. 1. 



1 This is the same as the ' vanishing-point ' of perspective. 



6 CIRCLES OF THE CELESTIAL SPHERE. [§ 8 

or Dipper-handle, is about 16° long, and the long side of the 
Dipper-bowl is about 10° ; the moon and the sun are each 
about half a degree, or 30 ', in diameter. 

It is very important that the student in Astronomy should become 
accustomed as soon as possible to estimate celestial measures in this 
way. A little practice soon makes it easy, though at first one is apt 
to be embarrassed by the fact that the sky looks to the eye not like a 
true hemisphere but like a flattened vault, so that the estimates of 
distances for all objects near the horizon are apt to be too large. The 
moon, when rising or setting, looks to most persons much larger than 
when overhead ; and the Dipper-bowl, when underneath the pole, seems 
to cover a much larger area than when above it. 

9. Circles and Principal Points of the Celestial Sphere. — 

Just as the surface of the earth in Geography is covered with 
a net-work of imaginary lines, — meridians and parallels of 
latitude, — so the sky is supposed to be marked off in a some- 
what similar way. Two such sets of points and reference 
circles are in common use to describe the apparent places of 
the stars, and a third was used by the ancients and is still em- 
ployed for some purposes. The first system depends upon the 
direction of the force of gravity shown by a plumb-line at the 
point where the observer stands ; the second upon the direc- 
tion of the axis of the earth, which points very near the so- 
called Pole-star ; and the third depends upon the position of 
the orbit in which the earth travels around the sun. 

10. The Gravitational or Up-and-Down System. — (a) The 

Zenith and Nadir. The point in the sky directly above the 
observer is called the zenith; the opposite point, under the 
earth and of course invisible, the nadir. 1 

(b) The Horizon (pronounced ho-ii'-zon, not hor'-i-zon). 

1 These are Arabic terms. About 1100 a.d. the Arabs were the 
world's chief astronomers, and have left their mark upon the science in 
numerous names of stars and astronomical terms. 



10] 



VERTICAL CIRCLES. 



This is a ' great circle ' * around the sky, half-way between the 
zenith and the nadir, and therefore everywhere 90° from the 
zenith. The word is derived from a Greek word which means 
a 'boundary'; i.e., the line where the earth or sea limits the 
sky. The actual line of division, which on the land is always 
more or less irregular, is called the visible horizon, to distin- 
guish it from the true horizon defined above. We may also 
define the horizon as the great circle where a plane which 
passes through the observer's eye perpendicular to the plumb- 
line cuts the celestial sphere. 

11. Vertical Circles and the Meridian; Altitude, and Azi- 
muth. — Circles drawn from the zenith to the nadir cut the 
horizon at right angles, and are known as vertical circles. Each 
star has at any moment its own vertical circle. 

z 




Fig. 2. — The Horizon and Vertical Circles. 
O, the place of the Observer. 
OZ, the Observer's Vertical. 
Z, the Zenith ; P, the Pole. 
SWiVE, the Horizon. 
SZPN y the Meridian. 
EZW, the Prime Vertical. 



M y some Star. 

ZMH, arc of the Star's Vertical Circle. 

TMR, the Star's Almucantar. 

Angle TZM, or arc Sff, Star's Azimuth. 

Arc HM, Star's Altitude. 

Arc ZM t Star's Zenith Distance. 



That particular vertical circle which passes north and south 
is known as the celestial meridian ; while the vertical circle 
at right angles to this is called the prime vertical. Small circles 

1 ' Great Circles \ are those which divide the sphere into two equal 
parts. 



8 DIURNAL ROTATION. C§ H 

drawn parallel to the horizon are known as parallels of alti- 
tude, or almucantars. Fig. 2 illustrates these circles. 

By their help we can easily define the apparent position of 
a heavenly body. 

Its Altitude is its apparent elevation above the horizon ; that 
is, the number of degrees between it and the horizon, measured 
on a vertical circle. Thus, in Fig. 2, the vertical circle ZMH 
passes through the point M. The arc MH, measured in 
degrees, is the altitude of M, and the arc ZM is called its 
zenith distance. 

The Azimuth of a heavenly body is the same as its 'bearing' 
in Surveying, but measured from the true meridian and not 
from the magnetic. 1 It is the arc of the horizon, measured in 
degrees, intercepted between the south point and the foot of 
the vertical circle which passes through the object. 

There are various ways of reckoning azimuth. Many writ- 
ers express it in the same way as the ' bearing , in Surveying, 
i.e., so many degrees east or west of north or south. In the 
figure, the azimuth of M thus expressed is about 8, 50° E. 
The more usual way at present, however, is to reckon clear 
around from the south, through the west, to the point of be- 
ginning. Expressed in this way the azimuth of M would be 
about 310°, — i.e., the arc S WNEH. 

Altitude and azimuth, however, are inconvenient for many 
purposes, because they continually change for a celestial object 
as it moves across the sky. 

12. The Apparent Diurnal Rotation of the Heavens. — If we 

go out on some clear evening in the early autumn, say about 
the 22d of September, and face the north, we shall find the ap- 
pearance of that part of the heavens directly before us substan- 
tially as shown' in Fig. 3. In the north is the constellation of 

1 The reader is reminded that the magnetic needle does not point 
exactly north. Its direction varies widely at different parts of the earth, 
an I, moreover, is continually changing to some extent. 



§12] 



DIURNAL ROTATION. 



9 



the Great Bear (Ursa Major), characterized by the conspicuous 
group of seven stars known as the " Great Dipper." It now 
lies with its handle sloping upward to the west. The two 
easternmost stars of the four which form its bowl are called 



d^ 



xjx 



V 



snuon 



&/ 






A^ 






V *> 



*\ 



g*\ 



* 



*V 



** 



P 



dP. 



/\V* 



x? 






** 



**. 




C/P 



$F 



^ 



C^ 



*M 



& 






-& 



J* 



*&> 



vtn 



Fig. 3. — The Northern Circumpolar Constellations. 

the " Pointers/' because they point to the Pole-star, which is a 
solitary star not quite half-way from the horizon to the zenith 
(in the latitude of New York), and about as bright as the 
brighter of the two Pointers. 

High up on the opposite side of the Pole-star from the 
Great Dipper, and at nearly the same distance, is an irregular 



10 DIURNAL ROTATION. [§ 12 

zigzag of five stars, each about as bright as the Pole-star itself. 
This is the constellation of Cassiopeia. 

If now we watch these stars for only a few hours, Ave shall 
find that while all the forms remain unaltered, their places in 
the sky are slowly changing. The Great Dipper slides down- 
ward towards the north, so that by eleven o'clock (on Sept. 
22) the Pointers are directly under the Pole-star. Cassiopeia 
still keeps opposite, however, rising towards the zenith; and 
if we continue the watch through the whole night, we shall 
find that all the stars appear to be moving in circles around a 
point near the Pole-star, revolving in the opposite direction to 
the hands of a watch (as we look towards the north) with a 
steady motion which takes them completely around once a day, 
or, to be more exact, once in 23 h 56 m 4.1 s of ordinary time. 
They behave just as if they were attached to the inner surface 
of a huge revolving sphere. 

To indicate the position of the stars as it will be at midnight of 
Sept. 22, the figure must be held so that XII in the margin is at the 
bottom; at 4 a.m. the stars will have come to the position indicated 
by bringing XVI to the bottom, and so on. But at eight o'clock on 
the next night we shall find things in their original position very 
nearly. 

If instead of looking toward the north we now look south- 
ward, we shall find that in that part of the sky also the stars 
appear to move in the same kind of way. All that are not too 
near the Pole-star rise somewhere in the eastern horizon, 
ascend obliquely to the meridian, and descend to their setting 
at points on the western horizon. The next day they rise and 
set again at precisely the same points, and the motion is 
always in an arc of a circle, called the star's diurnal circle, the 
size of which depends upon its distance from the pole. More- 
over, all of these arcs are strictly concentric. 

The ancients accounted for these fundamental and obvious 
facts by supposing that the stars are really fastened to the 



§ 12] DEFINITION OF THE POLES. 11 

celestial sphere, and that this sphere really turns daily in the 
manner indicated. According to this view there must really 
be upon the sphere two opposite points which remain at rest, 
and these are the poles. 

13. Definition of the Poles. — The Poles, therefore, may be 
defined as those two points in the sky where a star would have 
no diurnal motion. The exact position of either pole may be 
determined with proper instruments, by finding the centre of 
the small diurnal circle described by some star near it, as, for 
instance, by the Pole-star. 

The student must be careful not to confound the Pole with 
the Pole-star. The pole is an imaginary point; the Pole- 
star is only that one of the conspicuous stars which happens 
now 1 to be nearest to that point. The Pole-star at present is 
about 1\° distant from it. If we draw an imaginary line from 
the Pole-star to the star Mizar (the one at the bend of the 
Dipper-handle), it will pass almost exactly through the pole 
itself ; the distance of the pole from the Pole-star being very 
nearly one-quarter of the distance between the two " Pointers." 

This definition of the pole is that which would be given by 
one familiar with the sky, but ignorant of the earth's rotation, 
and it is still perfectly correct ; but knowing, as we now do, 
that this apparent revolution of the celestial sphere is due to 
the real spinning of the earth on its axis, we may also define 
the poles as the two points where the earth's axis of rotation, 
produced indefinitely, would pierce the celestial sphere. 

Since the two poles are diametrically opposite in the sky, only one 
of them is usually visible from any given place. Observers north of 
the earth's equator see only the north pole, and vice versa for observ- 
ers in the southern hemisphere. 

14. The Celestial Equator, or Equinoctial; Declination. — 

The Equator is a great circle of the celestial sphere drawn 
half-way between the poles, everywhere 90° from each of them, 

1 See Article 126. 




12 HOUR-CIRCLES. [§ 14 

and is the great circle in which the plane of the earth's equator 
cuts the celestial sphere. It is often called the Equinoctial. 
Fig. 4 shows how the plane of the earth's equator produced 
far enough would mark out such a circle in the heavens. 

Small circles drawn parallel 
to the equinoctial, like the paral- 
lels of latitude on the earth, are 
known as 'Parallels of Decli- 
nationj the Declination of a star 
being its distance in degrees 
north or south of the celestial 
equator, -f- if north, — if south. 
It corresponds precisely with 
the latitude of a place on the 
earth's surface ; but it cannot be 

Fig. 4. — The Plane of the Earth's Equa- Called Celestial latitude, because 

tor produced to cut the Celestial Sphere. ^at term has been preoccupied 
for an entirely different quantity (Art. 20). A star's parallel 
of declination is identical with its diurnal circle. 

15. Hour-Circles. — The great circles of the celestial sphere 
which pass through the poles like the meridians on the earth, 
and are therefore perpendicular to the celestial equator, are 
called Hour-Circles. Some writers call them celestial merid- 
ians, but the term is objectionable since it is sometimes used 
to indicate an entirely different set of circles. That particu- 
lar hour-circle which at any moment passes through the zenith 
of course coincides with the celestial meridian already defined 
in Art. 11. 

16. The Celestial Meridian and the Cardinal Points. — The 

best definition of the celestial meridian is, however, the great 
circle which passes through the zenith and the poles. The points 
where this meridian cuts the horizon (the circle of level), are 
the north and south points, and the east and west points of 



§16] 



THE VERNAL EQUINOX. 



13 



the horizon lie half-way between them, the four being known 
as the " Cardinal Points." The student is especially cautioned 
against confounding the north point with the north pole. The 
north point is on the horizon ; the north pole is high up in the 
sky. 




Fig. 5. — Equator, Hour-Circles, etc. 



0, place of the Observer; Z, his Zenith. 

SENW, the Horizon. 

POP', line parallel to the axis of the Earth. 

P and P' y the two Poles of the Heavens. 

EQ WT, the Celestial Equator, or Equinoc- 
tial. 

X, the Vernal Equinox, or " First of 
Aries." 

PXP', the Equinoctial Colure, or Zero 
Hour-Circle. 



m, some Star. 

Ym, the Star's Declination; Pm t its North- 
Polar Distance. 

Angle mPR = arc Q Y, the Star's (eastern) 
Hour-Angle ; = 24 h minus Star's 
western Hour- Angle. 

Angle XPm = arc XY t Star's Right Ascen- 
sion. 

Sidereal time at the moment = 24 h minus 
XPQ. 



In Fig. 5, P is the north celestial pole, Z is the zenith, and 
SQZPN is the celestial meridian. P and P are the poles, 
PmP is the hour-circle of m, and amRb V is its parallel of 
declination, or diurnal circle. N and 8 are the north and 
south points respectively. In the figure, m^Tis the declination 
of m, and mP is called its polar distance. 

17. The Vernal Equinox, or First of Aries. — In order to 
use this system of circles as a means of designating the places 



14 RIGHT ASCENSION. [§ 17 

of stars in the sky, it is necessary to fix upon some one hour- 
circle, to be reckoned from in the same way that the meridian 
of Greenwich is used on the earth's surface. The "Green- 
wich of the sky " which has thus been fixed upon, is the point 
where the sun crosses the celestial equator in the spring. 
The sun and moon and the planets do not behave as if they, 
like the stars, were firmly fixed upon the celestial sphere, but 
rather as if they were glow-worms crawling slowly about upon 
its surface while it carries them in its diurnal rotation. As 
every one knows, the sun in winter is far to the south of the 
equator, and in the summer far to the north, apparently com- 
pleting a yearly circuit of the heavens on a path known as the 
ecliptic. It crosses the equator, therefore, twice a year, pass- 
ing from the south side of it to the north about March 20th, 
and always at the same point (neglecting for the present the 
effect of what is known as 'precession'). This point is called 
the ' Vernal Equinox,'' and is made the starting-point. Unfor- 
tunately it is not marked by any conspicuous star ; but a line 
drawn from the Pole-star through Beta Cassiopei'ae (the west- 
ernmost or " preceding" star in the zigzag) (see Map I.) and 
continued 90° from the pole, strikes very near it. In Fig. 5, 
X represents this point. It is often called the "First of 
Aries." 

18. Right Ascension. — The right ascension of a star is the 
arc of the celestial equator intercepted between the vernal equinox 
and the point where the star's hour-circle cuts the equator, and is 
reckoned always eastward from the equinox and completely 
around the circle. It may be expressed either in degrees or 
in hours. 1 A star one degree west of the equinox has a right 
ascension of 359°, or of 23 h 56 m . Evidently the diurnal 
motion does not affect the right ascension of a star, but this, 
like the declination, remains practically unchanged for years. 
In Fig. 5, if X be the vernal equinox the right ascension of m 
is the arc XY measured from X eastward. 



1 Twenty-four hours = 360°; one hour = 15°. 



§ 19] SUMMARY. 15 

19. Thus we can define the position of a star either by its 
altitude and azimuth, which tell how high it is in the sky, and 
how it " bears," as a sailor would say ; or we may use its 
right ascension and declination, which do not change from 
day to day (not perceptibly at least), and so are better adapted 
to mapping purposes, corresponding as they do precisely to 
latitude and longitude upon the surface of the earth. 

Perhaps the easiest way to think of these celestial circles is 
the following : Imagine a tall pole standing straight up from 
the observer, having attached to it at the top (the zenith) two 
half circles coming down to the level of the observer's eye, one 
of them running north and south (the meridian), and the 
other east and west (the prime vertical). The bottoms of 
these two semicircles are connected by a complete circle, the 
horizon, at the level of the eye. This framework, immense 
but fortunately only imaginary and so not burdensome, the 
observer takes with him wherever he goes, keeping always at 
its centre, while over it turns the celestial sphere ; more 
strictly, he and the earth and his framework turn together 
under the celestial sphere. 

The circles of the other set are drawn upon the celestial 
sphere itself (the equator and the hour-circles) and are not 
affected at all by the observer's journeys, but are as fixed as 
the poles and meridians upon the earth; the stars also, to all 
ordinary observation, are fixed upon the sphere just as cities 
are upon the earth. They really move, of course, and swiftly, 
as has been said before, but they are so far away that it takes 
centuries, as a rule, to produce the slightest apparent change 
of place. 

20. Celestial Latitude and Longitude. — A different way of desig- 
nating the positions of the heavenly bodies in the sky has come down 
to us from very ancient times. Instead of the equator it makes use 
of another circle of reference in the sky, known as the ' Ecliptic.' 
This is simply the apparent path described by the sun in its annual 
motion among the stars ; for the sun appears to creep around the 



16 CELESTIAL LATITUDE AND LONGITUDE. [§ 20 

celestial sphere in a circle once every year, and the Ecliptic may be 
defined as the intersection of the plane of the earth's orbit with the 
celestial sphere, just as the celestial equator is the intersection of the 
earth's equator : the vernal equinox is one of the points where the two 
circles cross. Before the days of clocks, the Ecliptic was in many 
respects a more convenient circle of reference than the equator and 
was almost universally used as such by the old astronomers. Celestial 
longitude and latitude are measured with reference to the Ecliptic, in 
the same way that right ascension and declination are measured with 
respect to the equator. Too much care can hardly be taken to avoid 
confusion between terrestrial latitude and longitude and the celestial 
quantities that bear the jiuiie name. 



URANOGRAPHYo 



17 



CHAPTER II. 

URANOGRAPHY. 

GLOBES AND STAR-MAPS. — STAR MAGNITUDES. — DESIG- 
NATION OF THE STARS. — THE CONSTELLATIONS. 

Note. — It is hardly necessary to say that this chapter is to be treated 
by the teacher differently from the rest of the book. It is to be dealt 
with, not as recitation matter, but as field-work : to be taken up at differ- 
ent times during the course as the constellations make their appearance 
in the evening sky. 

For convenience of reference we add the following alphabetical list of 
the constellations described or mentioned in the chapter : — 









Article 




Article 


Andromeda . . . . 35 


Cepheus 


. 29 


Anser, see Vulpecula 




. 69 


Cetus .... 


. 39 


Antinotis, see Aquila 




. 71 


Coma Berenices 


. 57 


Antlia 




. 62 


Columba 


. 45 


Aquarius . 






. 78 


Corona Borealis . 


. 60 


Aquila 






. 71 


Corvus 


. 55 


Argo Navis 






. 51 


Crater 


. 55 


Aries . 






. 38 


Cygnus 


. 68 


Auriga 






. 41 


Delphlnus . 


. 74 


Bootes 






. 59 


Draco .... 


. 30 


Camelopardus 






. 31 


Equiileus . 


. 75 


Cancer 






. 52 


Eridanus . 


. 44 


Canes Yenatici 






. 58 


Gemini 


. 47 


Canis Major 






. 49 


Grus .... 


. 79 


Canis Minor 






. 48 


Hercules . 


. 66 


Capricornus 






. 73 


Hydra 


. 55 


Cassiopeia . 






. 28 


Lacerta 


. 76 


Centaurus . 






. 62 


Leo ..... 


. 53 



18 



GLOBES AND STAK-MAPS. 



[§21 









Article 




Article 


Leo Minor 54 


(Pleiades) .... 


. 42 


Lepus 






. 45 


Sagitta .... 


. 70 


Libra . 






. 61 


Sagittarius .... 


. 72 


Lupus 






. 62 


Scorpio 


. 63 


Lynx . 






. 46 


Sculptor .... 


. 39 


Lyra . 






. 67 


Serpens .... 


. 65 


Monoceros 






. 50 


Serpentarius, see Ophiuchus 


. 65 


Norma 






. 64 


Sextans 


. 54 


Ophiiichus 






. 65 


Taurus .... 


. 42 


Orion . 






. 43 


Taurus Poniatovii 


. 65 


Pegasus 






. 77 


Triangulum 


. 37 


Perseus 






. 40 


Ursa Major 


. 26 


Phoenix 






. 39 


Ursa Minor 


. 27 


Pisces 






. 36 


Virgo 


. 56 


Piscis Austi 


-alis . 




. 79 


Vulpecula . . . 


. 69 



21. Globes and Star-Maps. — In order to study the constel- 
lations conveniently, it is necessary to have either a celestial 
globe or a star-map, by which to identify the stars. The globe 
is better and more accurate, if of sufficient size ; but is costly 
and rather inconvenient. (For a figure and description of the 
globe, see Appendix, Art. 400.) For most purposes a star-map 
will answer just as well as the globe, but it can never repre- 
sent any considerable portion of the sky correctly without 
more or less distortion of all the lines and figures near the 
margin of the map. Such maps are made on various systems, 
each presenting its own advantages. In all of them the 
heavens are represented as seen from the inside, and not as on 
the globe, which represents the sky as seen from the outside. 

22. Star-Maps of this Book. — We present a series of four 
small maps, which, though hardly on a large enough scale to 
answer every purpose of a complete celestial atlas, are quite 
sufficient to enable the student to trace out the constellations, 
and to identify the principal stars. In the map of the north 
circumpolar regions, Map I., the pole is in the centre, and at 
the circumference are numbered the twenty-four right ascension 



§ 22 ] STAR MAGNITUDES. . 19 

hours. The parallels of declination are represented by equi- 
distant concentric circles. On the three other rectangular 
maps, which show the equatorial belt of the heavens lying 
between 50° north and 50° south of the equator, the parallels 
of declination are horizontal lines, while the hour-circles are 
represented by vertical lines, also equidistant, but spaced at 
a distance which is correct, not at the equator but for declina- 
tion 35°. This keeps the distortion within reasonable bounds, 
even near the margin of the map, and makes it very easy to 
lay off the places of any object for which the right ascension 
and declination are given. The ecliptic is the curved line 
which extends across the middle of the map. The top of the 
map is north ; and the east, instead of being at the right hand, 
as in a map of the earth's surface, is to the left, so that if the 
observer faces the south, and holds the map up before and 
above him, the constellations which are near the meridian will 
be pretty truly represented. 

The hours of right ascension are indicated on the central horizontal 
line, which is the celestial equator, and at the top of the map are given 
the names of the months. The word " September," for instance, means 
that the stars which are directly under it on the map will be near the 
meridian about 9 o'clock in the evening during that month. 

23. Star Magnitudes. — To the eye the principal difference 
in the appearance of the different stars is in their brightness, 
or their so-called ' magnitude.' Hipparchus (b.c. 125) and 
Ptolemy divided the visible stars into six classes, the brightest 
fifteen or twenty being called first-magnitude stars, and the 
faintest which can be seen by the naked eye being called 
sixth. 

It has since been found that the light of the average first-magnitude 
star is just about 100 times as great as that of the sixth ; and at this 
rate, the light of a first-magnitude star is just a trifle more than equal 
to two and a half second-magnitude stars, and a second-magnitude 
star to two and a half third-magnitude stars, etc. 



20 DESIGNATION OF THE STARS. [§ 23 

Our maps show all the stars down to about 4^ magnitude, 
about a thousand in number, and all which can be seen in a 
moonlight night. A few smaller stars are also iuserted where 
they mark some particular configuration or point out some 
interesting telescopic object. Such double Stars as can be ob- 
served by a three or four inch telescope are marked on the map 
by underscoring : two underscoring lines denote a triple star, 
and three a multiple. A variable star is denoted by a circle 
enclosing the star symbol. A few clusters and nebulae are also 
indicated. The letter M. against one of these stands for i Mes- 
sier/ who made the first catalogue of 103 such objects in 1784; 
e.g., 97 M. designates No. 97 on Messier's list. 

For reference purposes and for study of the heavens in detail, the 
more elaborate star-atlases of Proctor, Heis, or Klein are recommended, 
especially the latter, which contains a great amount of useful infor- 
mation in addition to the maps, and is very cheap compared with the 
others. The student or teacher who possesses a telescope will also find 
an invaluable accessory to it in Webb's " Celestial Objects for Common 
Telescopes." (Published by Longmans, Green and Co., N. Y.) 

24. Designation of the Stars. — A few of the brighter stars 
are designated by names of their own, and upon the map those 
names which are in most common use are indicated. Generally, 
however, the designation of visible stars is by the letters of 
the Greek alphabet, on a plan proposed in 1603 by Bayer, and 
ever since followed. The letters are ordinarily applied nearly 
in the order of brightness, Alpha being the brightest star in 
the constellation and Beta the next brightest; but they are 
sometimes applied to the stars in their order of position rather 
than in that of brightness. When the stars of a constellation 
are so numerous as to exhaust the letters of the Greek alpha- 
bet, the Boman letters are next used, — and then, if necessary, 
we employ the numbers which Flamsteed assigned a century 
later. At present every star visible to the naked eye can be 
referred to and identified by its number or letter in the con- 



, 



§24] URSA MAJOR. 21 

stellation to which, it belongs. For the Greek Alphabet, see 
page 344 (Appendix). 

25. We begin our study of Uranography with the constel- 
lations which are circumpolar (i.e., within 40° of the north 
pole), because these are always visible in the United States 
and so can be depended on to furnish land (or rather sky) 
marks to aid in tracing out the others. Since in the latitude 
of New York the elevation of the pole is about 41°, it follows 
that there (and this is nearly enough true of the rest of the 
United States) all the constellations which are within 41° of 
the north pole will move around it once in twenty-four hours 
without setting. For this reason they are called circumpolar. 
Map I. contains them all. 

26. XJrsa Major, the Great Bear (Map I.). — Of these circum- 
polar constellations none is more easily recognized than Ursa 
Major. Assuming the time of observation as about 8 o'clock 
in the evening on Sept. 22d, it will be found below the pole 
and to the west. Hold the map so that VIII. is at the bottom 
and it will be rightly placed for the time assumed. 

The familiar Dipper is sloping downward in the northwest, 
composed of seven stars, all of about the second magnitude, 
excepting Delta (at the junction of the handle to the bowl), 
which is of the third magnitude. The stars Alpha (Dubhe), 
and Beta (MeraJc), are known as the "'Pointers," because a 
line drawn from Beta through Alpha and produced about 30° 
passes very near the Pole-star. The dimensions of the Dipper 
furnish a convenient scale of angular measure. Prom Alpha 
to Beta is 5° ; from Alpha to Delta is 10° ; and from Alpha to 
Eta, at the extremity of the Dipper-handle, (which is also the 
Bear's tail,) is 26°. The Dipper (known also in England as 
the " Plough " and as the " Wain," or wagon) comprises but a 
small part of the whole constellation. The head of the Bear, 
indicated by a small group of scattered stars, is nearly on the 



22 URSA MAJOR. [§ 26 

line from Delta through Alpha, carried on about 15° ; at the 
time assumed (Sept. 22d, 8 o'clock) it is almost exactly under 
the pole. 

Three of the four paws of the creature are marked each by 
a pair of third or fourth magnitude stars 1-1° or 2° apart. The 
three pairs are nearly equidistant, about 20° apart, and almost 
on a straight line parallel to the diagonal of the Dipper-bowl 
from Alpha to Gramma, but some 20° south of it. At the time 
assumed they are all three very near the horizon for an ob- 
server in latitude 40°, but during the spring or summer, when 
the constellation is high in the sky, they can be easily made 
out. 

The star Zeta (or Mizar), at the bend in the handle, is 
easily recognized by the little star Alcor near it. Mizar it- 
self is a double star, easily seen as double with a small tel- 
escope, and one of the most interesting recent astronomical 
results is the discovery that it is really triple, the larger of 
the two stars being itself double, invisibly so to the telescope, 
but revealing its double character by means of the lines in 
its spectrum (see Art. 373). The star Xi, the southern one of 
the pair, which marks the left-hand paw, is also double and 
binary, i.e., the two stars which compose it revolve about their 
common centre of gravity in about sixty-one years. (For 
diagram of the orbit, see Fig. 77, Art. 369.) It was the first 
binary whose orbit was computed. 

According to the ancient legends, Ursa Major is Callisto, the daugh- 
ter of Lycaon, king of Arcadia. The jealousy of Juno 1 changed her 
into a bear, and afterwards Jupiter placed her among the constella- 
tions with Areas her son, who became Ursa Minor. One of the quaint 



1 We have followed throughout the Roman nomenclature of the gods 
and heroes, as used by Virgil and Ovid ; but the reader should be reminded 
that, in many important respects, these Roman personages differ from 
the Greek divinities who were identified with them. It should be said, 
also, that in many cases the old legends are greatly confused and often 
contradictory, as, for instance, in the case of Hercules. 



§27] URSA MINOR. 23 

old authors explains the very un-bearlike length of the creatures' tails, 
by saying that they stretched as Jupiter lifted them to the sky. 

27. Ursa Minor, the Lesser Bear (Map I.). — The line of the 
" Pointers " unmistakably marks out the Pole-star (Polaris), 
a star of the second magnitude, standing quite alone. It is 
at the end of the tail of Ursa Minor, or at the extremity of 
the handle of the " Little Dipper " ; for in Ursa Minor, also, 
the seven principal stars form a dipper, though with the handle 
bent in a different way from that of the other dipper. Begin- 
ning at Polaris, a curved line (concave towards Ursa Major) 
drawn through Delta and Epsilon brings us to Zet.a, where the 
handle joins the bowl. Two bright stars (second and third 
magnitude), Beta and Gamma, correspond to the Pointers in 
the large Dipper, and are known as the " Guardians of the 
Pole " ; Beta is named Kochab. The pole now lies about 1^° 
from the Pole-star, on the line joining it to Mizar (at the 
bend in the handle of the large Dipper). 

It has not always been so. Some 4000 years ago the star Thuban 
(Alpha Draconis) was the Pole-star, and 2000 years ago the present 
Pole-star was very much farther from the pole than now. At present 
the pole is coming nearer to the star, and towards the close of the 
next century it will be within half a degree of it. Twelve thousand 
years hence the bright star Alpha Lyrse will be the Pole-star, — and 
this not because the stars change their positions, but because the axis 
of the earth slowly changes its direction, owing to 'precession ' (see 
Art. 125). 

The Greek name of the Pole-star was Cynosura, which 
means the 'tail of the Dog,' indicating that at one time the 
constellation was understood to represent a Dog instead of a 
Bear. 

As already said (Art. 26) this constellation is by many writers 
identified with Areas, Callisto's son. But more generally Areas is 
identified with Bootes. 

The Pole-star is double, having a small companion barely 
visible with a telescope of two or three inches diameter. 



24 CASSIOPEIA, [§ 28 

28. Cassiopeia (Map I.). — This constellation lies on the op- 
posite side of the pole from the Dipper, and at about the same 
distance from it as the " Pointers." It is easily recognized by 
the zigzag, " rail-fence " configuration of the five or six bright 
stars that mark it. With the help of the rather inconspicuous 
star Kappa, one can make out of them a pretty good chair with 
the feet turned away from the pole. But this is wrong. In the 
recognized figures of the constellation the lady sits with feet 
towards the pole, and the bright star Alpha is in her bosom, 
while Zeta and the other faint stars south of Alpha are in her 
head and uplifted arms ; Iota, on the line from Delta to Epsilon 
produced, is in the foot. The order of the principal stars is 
easily remembered by the word 'Bagdei/ i.e., Beta, Alpha, 
Gamma, Delta, Epsilon, Iota. 

Alpha, which is slightly variable in brightness, is known as 
Schedir ; Beta is called Capli. The little star Eta, which is 
about half-way between Alpha and Gamma, a little off the 
line, is a very pretty double star, — the larger star orange, the 
smaller one purple. It is binary (i.e., the two stars revolve 
around each other), with a period of about 206 years. 

In the year 1572 a famous temporary star made its appear- 
ance in this constellation, at a point on the line drawn from 
Gamma through Kappa, and extended about half its length. 
It was carefully observed and described by Tycho Brahe, and 
at one time was bright enough to be seen easily in broad day- 
light. There has been an entirely unfounded notion that this 
was identical with the Star of Bethlehem, and there has been 
an equally unfounded impression that its reappearance may be 
expected about the present time. 

Cassiopeia was the wife of Cepheus, king of Libya, and the mother 
of Andromeda, who was rescued from the sea-monster, Cetus, by Per- 
seus, who came flying through the air, and used the head of Medusa, 
(which he still holds in his hand,) to turn his adversaries to stone. 
Cassiopeia had indulged in too great boasting of her daughter's beauty, 



§ 29] CEPHEUS — DBACO. 25 

and thus excited the jealousy of the Nereids, at whose instigation the 
sea-monster was sent by Neptune to ravage the kingdom. 

29. Cepheus (Map I.). — This constellation, though large, 
contains very few bright stars. At* the assumed time (8 
o'clock, Sept. 22d) it is above Cassiopeia and to the west, not 
having quite reached the meridian above the pole. A line 
carried from Alpha Cassiopeia through Beta, and produced 20°, 
will pass very near to Alpha Cephei, a star of the third 
magnitude in the king's right shoulder. Beta Cephei is about 
8° north of Alpha, and Gamma about 12° from Beta, both also 
of the third magnitude. Gamma is so placed that it is at the 
obtuse angle of a rather flat isosceles triangle of which Beta 
Cephei and the Pole-star form the other two corners. Cepheus 
is represented as sitting behind Cassiopeia (his wife) with his 
feet upon the tail of the Little Bear, Gamma being in his left 
knee. His head is marked by a little triangle of fourth- 
magnitude stars, of which Delta is a remarkable variable with 
a period of 5-J- days. It is also a spectroscopic binary (Art. 
373). There are also several other telescopic variables in the 
same neighborhood. Beta is a very pretty and easy double- 
star. 

30. Draco, the Dragon (Map I.). — The constellation of 
Draco is characterized by a long, winding line of stars, mostly 
small, extending half-way around the pole and separating the 
two Bears. A line from Delta Cassiopeia drawn through Beta 
Cephei and extended about as far again will fall upon the head 
of Draco, marked by an irregular quadrilateral of stars, two 
of which are of the 2\ and 3 magnitude. These two bright 
stars about 4° apart are Beta and Gamma. The latter (named 
Etanin), in its daily revolution, passes almost exactly through, 
the zenith of Greenwich, and it was by observations upon it 
that the " aberration of light " was discovered (see Art. 435). 
The nose of Draco is marked by a smaller star, Mu, some 
5° beyond Beta, nearly on the line drawn through it from 



26 DRACO. [§ 30 

Gamma. From Gamma we trace the neck of Draco, eastward 
and downward * toward the Pole-star, until we come to Delta 
and Epsilon and some smaller stars near them. 

There the direction of the line is reversed, as shown upon the 
map, so that the body of the monster lies between its own head 
and the bowl of the Little Dipper, and winds around this bowl 
until the tip of the tail is reached, at the middle of the line 
between the Pointers and the Pole-star. The constellation 
covers more than 12 hours of right ascension. 

One star deserves special notice, the star Alpha or Thuban, 
a star of 3^ magnitude, which lies half-way between Zeta Ursae 
Majoris (Mizar) and Gamma Ursa Minoris. Four thousand 
seven hundred years ago it was the Pole-star, and then within 
a quarter of a degree of the pole, much nearer than Polaris is 
at present or ever will be. It is probable also that its bright- 
ness has considerably fallen off within the last 200 years, since 
among the ancient astronomers it was always reckoned as of 
the second magnitude and is not now much above the fourth. 
The so-called 'Pole of the Ecliptic' is in this constellation, 
i.e., the point which is 90° distant from every point in the 
Ecliptic, the circle annually described by the sun. This point 
(see map) is the centre around which precession causes the 
pole to move nearly in a circle (see Art. 126) once in 25,800 
years. 

The mythology of this constellation is doubtful. According to 
some it is the dragon which Cadmus slew, afterwards sowing its teeth, 
from which sprung up the harvest of armed men who fought and slew 
each other, leaving only the five survivors who were the founders of 
Thebes. Others say that it was the dragon who watched the golden 
apples of the Hesperides, and was killed by Hercules when he cap- 
tured that prize. This accords best with the fact that in the heavens 
Hercules has his foot on the dragon's head. 

1 The description applies strictly only at the time assumed, 8 o'clock, 
Sept. 22d. 






§ 31] THE MILKY WAY. 27 

31. Camelopardus. — This is the only remaining one of the strictly 
circumpolar constellations, — a modern one containing no stars above 
fourth magnitude, and established by Hevelius (1611-1687) simply to 
cover the great empty space between Cassiopeia and Perseus on one 
side, and Ursa Major and Draco on the other. The animal stands on 
the head and shoulders of Auriga, and his head is between the Pole- 
star and the tip of the tail of Draco. 

The two constellations of Perseus (which at the time assumed is 
some 20° below Cassiopeia), and of Auriga, are partly circumpolar, but 
on the whole can be more conveniently treated in connection with the 
equatorial maps. Capella, the brightest star of Auriga, and next to 
Vega and Arcturus the brightest star in the northern hemisphere, 
is at the time assumed (Sept. 22d, 8 o'clock) a few degrees above 
the horizon in the N\E. Between it and the nose of Ursa Major lies 
part of the constellation of the Lynx, a modern one, made, like 
Camelopardus, by Hevelius, merely to fill a gap, and without airy 
large stars. 

32. The Milky Way in the Circumpolar Region. — The only 
circumpolar constellations traversed by the Milky Way are 
Cassiopeia and Cepheus. It enters the circumpolar region from 
the constellation of Cygnus, which at this time is just in the 
zenith, sweeps down across the head and shoulders of Cepheus, 
and on through Cassiopeia and Perseus to the northeastern 
horizon in Auriga. There is one very bright patch a few 
degrees north of Beta Cassiopeiae, and half way between Delta 
Cassiopeiae and Gramma Persei there is another bright cloud 
in which is the famous double cluster of the " Sword-handle 
of Perseus," — a beautiful object for even the smallest tele- 
scope. 

33. For the most part the constellations shown upon the 
circumpolar map (P^ will be visible every night in the north- 
ern part of the United States. At places farther south the con- 
stellations near the rim of the map will stay below the horizon 
for a short time every tw r enty-four hours, since the height of 
the pole always equals the latitude of the observer, and there- 
fore only those stars which have a polar distance less than the 



28 TIMES FOR OBSERVATION*, [§ 33 

latitude will remain constantly visible. In other words, if, 
with, the pole as a centre, we draw a circle with a radius equal 
to the height of the pole above the horizon, all the stars within 
this circle will remain continually above the horizon. This is 
called the circle of ' Perpetual Apparition/ (Art. 85.) At 
New Orleans, in latitude 30°, its radius, therefore, is only 30°, 
and only those stars which are within 30° of the pole will 
make a complete circle without setting. At stations in the 
northern part of the United States, as Tacoma, it is nearly as 
large as the whole map. 

34. Before proceeding to consider the other constellations, 
the student should be reminded that he will have to select 
those that are conveniently visible at the time of the year 
when he happens to be studying the subject, and that, if he 
wishes to cover the whole sky, he will have to take up the sub- 
ject more than once, and at various seasons of the year. The 
constellations near the southern limits of the map especially 
can be seen only a few weeks in each year. 

He will also be likely to be occasionally perplexed by find- 
ing in the heavens certain conspicuous stars not given on the 
maps, — stars much brighter than any that are given. These 
are the planets Venus, Jupiter, Mars, and Saturn, called planets, 
i.e., ' wandering stars/ just because they continually change 
their place, and so cannot be mapped. The student will find 
it interesting and instructive, however, to dot down upon the 
star-map every clear night the places of any planets he may 
notice, and thus to follow their motion for a month or two. 

Remember also that on these maps east always lies on the 
left hand, so that the map should be held between the eye and 
the sky in order to represent things correctly. We begin with 
Andromeda at the N.W. corner of Map II. 

35. Andromeda (Maps II. and IV.). Nov. — Andromeda will 
be found exactly overhead in our latitudes about 9 o'clock in 



§ 35] ANDROMEDA — PISCES. 29 

the middle of November. Its characteristic configuration is the 
line of three second-magnitude stars, Alpha, Beta, and Gamma, 
extending east and north from Alpha, (Alpheratz) which 
itself forms the N.E. corner of the so-called "Great Square 
of Pegasus," and is sometimes lettered as Delta Pegasi. This 
star may readily be found by extending an imaginary line from 
Polaris through Beta Cassiopeise, and producing it about as 
far again : Alpha is in the head of Andromeda, Beta (Mirach) 
in her waist, and Gamma (AlmaacJi) in her left foot. A line 
drawn northwesterly from Beta, nearly at right angles to 
the line Beta Gamma, will pass through Mu at a distance of 
about 5°, and produced another 5° will strike the "great 
nebula," which is visible to the naked eye like a little cloud of 
light, and forms a small obtuse-angled triangle with Nu and 
a little sixth-magnitude star. Andromeda has her mother, 
Cassiopeia, close by on the north, with her father, Cepheus, 
not far away, while at her feet is Perseus, her deliverer. Her 
head rests upon the shoulder of Pegasus. In the south, 
beyond the constellations of Aries and Pisces, Cetus, the sea- 
monster, who was to have devoured her, stretches his ungainly 
bulk. 

We have already mentioned the nebula. Another very pretty 
object is Gamma, which in a small instrument is a double star, the 
larger one orange, the smaller a greenish blue. The small star is itself 
double, making the system really triple, but as such is beyond the 
reach of any but very large instruments. 

When Neptune sent the leviathan, Cetus, to ravage Libya, the ora- 
cle of Ammon announced that the kingdom could be delivered only 
if Cepheus would give up his daughter. He assented and chained the 
poor girl to a rock to await her destruction. But Perseus, returning 
through the air from the slaying of the Gorgon, Medusa, saw her, 
rescued her, won her love, and made her his wife. 

36. Pisces, the Fishes (Maps II. and IV.). Nov.— Immediately 
south of Andromeda lies Pisces, the first of the constellations 



30 TRIANGULUM. [§ 36 

of the Zodiac, 1 which is a belt 16° wide (8° on each side of 
the ecliptic) encircling the heavens, and including the space 
within the limits of which the sun, the moon, and all the prin- 
cipal planets perform their apparent motions. At present, in 
consequence of precession, it occupies the sign of Aries (see 
Art. 126). It has not a single conspicuous star, and is notable 
only as now containing the Vernal Equinox, or "First of 
Aries" which lies near the southern boundary of the constel- 
lation in a peculiarly starless region. A line from Alpha An- 
dromedae through Gamma Pegasi, continued as far again, strikes 
about 2° east of the point. The body of one of the two fishes 
lies about 15° south of the middle of the southern side of the 
"Great Square of Pegasus," and is marked by an irregular 
polygon of small stars, 5° or 6° in diameter. A long, crooked 
"ribbon" of little stars runs eastward for more than 30°, 
terminating in Alpha Piscium, (called El Rischa, or 'the 
knot/) a star of the fourth magnitude 20° south of the head 
of Aries. Prom there another line of stars leads up north- 
west in the direction of Delta Andromedae to the northern 
fish, which lies in the vacant space south of Beta Andromedae. 

Alpha is a very pretty double star, the two components being about 
2 rf apart. 

The mythology of this constellation is not very well settled. One 
story is that the fishes are Venus and her son Cupid, who once were 
thus transformed when endeavoring to escape from the giant Typhon. 
The northern fish is Cupid, the southern his mother. 

37. Triangulum or Deltoton, the Triangle (Map II.). De- 
cember. — This little constellation, insignificant as it is, is one 
of Ptolemy's ancient forty-eight. It lies half-way between 
Gamma Andromedse and the head of Aries, and is character- 

1 The word is derived from the Greek word zoon, a living creature, 
and indicates that all the constellations in it (Libra alone excepted) are 
animals. The zodiacal constellations are for the most part of remote 
antiquity, antedating by many centuries even the Greek mythology. 



§ 38] ARIES — CETUS. 31 

ized by three stars of the third and fourth magnitude, easily 
made out by the help of the map. 

It may be regarded as a canonization of " Divine Geometry," but 
has no special mythological legend connected with it. 

38. Aries, the Ram (Map II). December. — This is the sec- 
ond of the zodiacal constellations, now occupying the sign of 
Taurus. It lies just south of Triangulum and Perseus. Its 
characteristic star-group is that composed of Alpha (Hamal), 
Beta, and Gamma (see map), ahout 20° due south of Gamma 
Andromedae. Alpha, a star of 2\ magnitude, is fairly conspic- 
uous, forming a large isosceles triangle with Beta and Gamma 
Andromedae. 

Gamma Arietis is a very pretty double star with the components 
about 9" apart. It is probably the first double star discovered, hav- 
ing been noticed by Hooke in 1664. 

The star 41 Arietis (3} magnitude), which forms a nearly equilat- 
eral triangle with Alpha Arietis and Gamma Trianguli, constitutes, 
with two or three other stars near it, the constellation of Musca 
(Borealis), a constellation, however, not now generally recognized. 

According to the Greeks, Aries is the ram which bore the golden 
fleece and dropped Helle into the Hellespont, when she and her brother, 
Phrixus, were flying on its back to Colchis. Long afterwards the 
Argonautic Expedition, with Jason as its head and Hercules as one 
of its members, sailed from Greece to Colchis to recover the fleece, 
and finally succeeded after long endeavors. 

39. Cetus, the Sea-monster (Maps II. and IV.). November- 
December. — South of Aries and Pisces lies the constellation 
of Cetus, the sea-monster ; which backs up into the sky from 
the southeastern horizon. The head lies some 20° southeast 
of Alpha Arietis, and is marked by an irregular five-sided fig- 
ure of stars, each side being some 5° or 6° long. The southern 
edge of this pentagon is formed by the stars Alpha or Menkar 
(2i magnitude) and Gamma (3 \ magnitude) ; Delta lies south- 
west of Gamma. Beta (Deneb Ceti), the brightest star of the 



32 PERSEUSo [§ 39 

constellation (2 magnitude) , stands by itself nearly 40° west 
and south, of Alpha. Gamma is a very pretty double star, but 
rather close for a small telescope, the components being only 
2.5" apart, yellow and blue. 

Cetus is the leviathan that was sent by Neptune to ravage Libya 
and devour Andromeda. Perseus turned him into stone by showing 
him the head of the Gorgon, Medusa. On the globes he is usually 
represented as a nondescript sort of beast, with a face like a puppy's, 
and a tightly curled tail; as if the Gorgon's head had frightened out 
all his savageness. 

South of Cetus lies the modern constellation of Sculptoris Appa- 
ratus (usually known simply as Sculptor), which, however, contains 
nothing that requires notice here. South of- Sculptor, and close to 
the horizon, even when on the meridian, is Phoenix. It has some 
bright stars, but none easily observable in the United States. 

40. Perseus (Maps I. and II.). January. — Eeturning now 
to the northern limit of the map, we come to the constella- 
tion of Perseus. Its principal star is Alpha (Algenib), rather 
brighter than the standard second magnitude, and situated 
very nearly on the prolongation of the line of the three chief 
stars of Andromeda. A very characteristic configuration is 
the so-called " segment of Perseus " (Map I.), a curved line 
formed by Delta, Alpha, Gamma, and Eta, with some smaller 
stars, concave towards the northeast, and running along the 
line of the Milky Way towards Cassiopeia. The remarkable 
variable star, Beta, or Algol, is situated about 9° south and a 
little west of Alpha, at the right angle of a right-angled triangle 
which it forms with Alpha Persei and Gamma Andromedse. 
Algol and a few small stars near it form " Medusa's Head," 
which Perseus carries in his hand. For further particulars 
and recent discoveries regarding this star, see Arts. 358 and 
360. 

Epsilon is a very pretty double star with the components about 8" 
apart ; but the most beautiful telescopic object in the constellation, 



§ 40] AUKIGA. 33 

perhaps the finest, indeed, in the whole heavens for a small telescope, 
is the pair of clusters about half-way between Gamma Persei and 
Delta Cassiopeiae, visible to the naked eye as a bright knot in the 
Milky Way, and already referred to in Art. 32. 

Perseus was the son of Danae by Jupiter, who won her in a shower 
of gold. He was sent by his enemies on the desperate venture of 
capturing the head of Medusa, the only mortal one of the three Gor- 
gons, which were frightful female monsters with wings, tremendous 
claws, and brazen teeth, and serpents for hair ; of such aspect that the 
sight turned all who looked at them to stone. The gods helped Per- 
seus by various gifts which enabled him to approach his victim, invis- 
ible and unsuspected, and to deal the fatal blow without looking at the 
sight himself. From the blood of Medusa, where her body fell, sprang 
Pegasus, the winged horse, and where the drops fell on the sands of 
Libya, as Perseus was flying across the desert, thousands of venomous 
serpents swarmed. On his way, returning home, he saw and rescued 
Andromeda, as already mentioned (Arts. 28 and 35). Hercules was 
one of their descendants. 

41. Auriga, the Charioteer (Maps I. and II.). January. — 
Proceeding east from Perseus we come to Auriga, who is 
represented as holding in his arms a goat and her kids. The 
constellation is instantly recognized by the bright yellow star, 
Capella (the Goat), and her attendant 'Hoedi' (the Kids). 
Alpha Aurigse (Capella) is, according to Pickering, precisely 
of the same brightness as Vega, both of them being about \ of 
a magnitude fainter than Arcturus, but distinctly brighter 
than any other stars visible, in our latitudes except Sirius itself. 
The spectroscope shows that Capella is very similar in charac- 
ter to our own sun, though probably vastly larger.- About 10° 
east of Capella is Beta Aurigae (Menkalinan) of the second 
magnitude ; Epsilon, Zeta, and Eta, which form a long triangle 
4° or 5° south of Alpha, are the Kids. 

There seems to be no well-settled mythological . history for this 
constellation, though some say that he is the charioteer of QEnomaus, 
king of Elis; while others connect him with the story of Phaeton, 
the son of Apollo, who borrowed the horses of his father and was over- 



34 TAUKUS. [§ 42 

thrown in mid-heaven. The goat is supposed to be Amalthea, the goafc 
which suckled Jupiter in his infancy. Capella and the Kids were al- 
ways regarded by astrologers as of kindly influence, especially towards 
sailors. 

42. Taurus, the Bull (Map II.). January. — This, the 
third of the zodiacal constellations, lies directly south of Per- 
seus and Auriga, and north of Orion. It is unmistakably 
characterized by the Pleiades, and by the V-shaped group of 
the Hyades which forms the face of the bull, with the red 
Aldebaran (Alpha Tauri), a standard first-magnitude star, 
blazing in the creature's eye, as he charges down upon Orion. 
His long horns reach out towards Gemini and Auriga, and 
are tipped with the second and third magnitude stars, Beta 
and Zeta. As in the case of Pegasus, only the head and 
shoulders appear in the constellation. Six of the Pleiades 
are easily visible, and on a dark night a fairly good eye will 
count nine of them. With a three-inch telescope about 100 
stars are visible in the cluster, which is more fully described 
with a figure in Art. 376. The brightest of the Pleiades is 
called ' Alcyone? and was assigned to the dignity of the 
< Central Sun' by Maedler (Art. 386). 

About 1° west and a little north of Zeta is a nebula (Messier 1), 
which has many times been discovered by tyros with a small telescope 
as a new comet : it is an excellent imitation of the real thing. 

According to the Greek legends, Taurus is the milk-white bull into 
which Jupiter changed himself when he carried away Europa from 
Phoenicia to the island of Crete, where she became the mother of 
Minos and the grandmother of Deucalion, the Noah of Greek my- 
thology. But Taurus, like most of the other zodiacal constellations, is 
really far older than the Greek mythology, and appears in the most 
ancient zodiacs of Egypt, where it was probably connected with the 
worship of the bull, Apis ; so also in the ancient Astronomy of Chal- 
dea and India. 

The Pleiades were daughters of the giant Atlas. Of the seven 
sisters, one, who married a mortal, lost her brightness, according 



§ 42] ORION. 35 

to the legend, so that only six remain visible. Some say that Merope 
was the one who thus gave up her immortality for love, but her star is 
still visible, while Celaeno and Asterope are both faint. The now rec- 
ognized names of the stars in the group (see map, Art. 376) include 
Atlas and Pleione, the parents of the family, as well as the seven sis- 
ters. As for the Hyades, who were half-sisters of the Pleiades, there 
is less legendary interest in their case. They are always called by 
the poets " the rainy Hyades." 

43. Orion (not O'rion) (Map II.). February. — This is the 
most splendid constellation in the heavens. As the giant 
stands facing the bull, his shoulders are marked by the two 
bright stars, Alpha (Betelgeuze) and Gamma (Bellatrix), the 
former of which in color closely matches Aldebaran, though 
its brightness is somewhat variable. In his left hand he holds 
up the lion skin, indicated by the curved line of little stars 
between Gamma and the Hyades. The top of the club, which 
he brandishes in his right hand, lies between Zeta Tauri and 
Mu and Eta Geminorum. His head is marked by a little tri- 
angle of stars of w r hich Lambda is the chief. His belt, through 
the northern end of which passes the celestial equator, consists 
of three stars of the second magnitude, pointing obliquely 
southeast toward Sirius. It is very nearly 3° in length, and 
is called the "Ell and Yard" or " Jacob's Staff." From the belt 
hangs the sword, composed of three smaller stars lying more 
nearly north and south : the middle one of them is the mul- 
tiple, Theta, in the great nebula, which even in a small tele- 
scope is a beautiful object, the finest nebula in the sky. Beta 
Orionis, or Rigel, a magnificent white star, is in the left foot, 
and Kappa is in the right knee. Orion has no right foot, or if 
he has, it is hidden behind Lepus. The quadrilateral Alpha, 
Gamma, Beta, Kappa, with the diagonal belt, Delta, Eta, Zeta, 
once learned can never be mistaken for anything else in the 
heavens. 

Rigel is a very pretty double star, the larger star having a very 
small companion about 10" distant. The two stars at the extremities 
of the belt are also double. 



36 LEPUS AND COLUMBA. [§ 43 

Orion was a giant and mighty hunter, son of Neptune, and beloved 
by both Aurora and Diana. The legends of his life and exploits are 
numerous, and often contradictory. He conquered every wild beast 
except the Scorpion, which stung and killed him. As a winter con- 
stellation his influence was counted stormy, and he was greatly dreaded 
by sailors. 

44. Eridanus, the River Po (Map II.). January. — This con- 
stellation lies south of Taurus, in the space between Cetus and Orion, 
and extends far below the southern horizon. The portion near the 
south pole has a pair of bright stars, which, of course, are never visi- 
ble at the United States. Starting with Beta (Cw*sa, as it is called), 
of the third magnitude, about 3° north and a little west of Rigel, one 
can follow a sinuous line of stars westward to the paws of Cetus, 
where the stream turns at right angles, and runs southward and south- 
west to the horizon. One can trace it, however, only by the help of a 
map on a larger scale than the one we present. 

45. Lepus and Columba (Map II.) . February. — The con- 
stellation of Lepus, the Hare, one of Orion's victims, is one 
of the ancient forty-eight, and lies just south of the giant, 
occupying a space of some 15° square. Its characteristic con- 
figuration is a quadrilateral of third and fourth magnitude 
stars, with sides from 3° to 5° long, about 10° south of Kappa 
Orionis, and 15° west of Sirius. 

Columba, the Dove, lies next south of Lepus, too far south 
to be well seen in the Northern States. Its principal star, 
Alpha (Phact) is of 2\ magnitude, and is readily found by 
drawing a line from Procyon to Sirius and prolonging it 
about the same distance. In passing, we may note that a 
similar line drawn from Alpha Orionis through Sirius, and 
produced, will strike near Zeta Argus, or Naos, a star about 
as bright as Phact, — the two lines which intersect at Sirius 
making the so-called "Egyptian X." 

Columba is a modern constellation, commemorating Noah's dove 
returning to the ark with the olive branch. 



§ 46] GEMINI — CANIS MINOR. 37 

46. Lynx (Maps L, II., and III.). February. — Returning now 
to the northern limit of the map, we find the modern constellation of 
the Lynx lying just east of Auriga, and enveloping it on the north 
and in the circumpolar region, as shown on the map. It contains no 
stars above the fourth magnitude, and is of no importance, except as 
occupying an otherwise vacant space. 

47. Gemini, the Twins (Map II.) . February and March. 
— This is the fourth of the zodiacal constellations, now lying 
mostly in the sign of Cancer. It contains the summer solstitial 
point — the point where the sun turns from its northern mo- 
tion to its southern in the summer. At present it is about 2° 
west and a little north of the star Eta. Gemini lies northeast 
of Orion and southeast of Auriga, and is sufficiently character- 
ized by the two stars Alpha and Beta (about 4^° apart), which 
mark the heads of the twins. The southern one, Beta, or 
Pollux, is now the brighter ; but Alpha, Castor, is much more 
interesting, as being double (easily seen with a small tele- 
scope). The feet are marked by the third-magnitude stars 
Gamma and Mu, some 10° east of Zeta Tauri. 

Castor and Pollux were the sons of Jupiter by Leda, and ancient 
mythology, especially that of Rome, is full of legends relating to them. 
Many of our readers will remember Macaulay's ballad of " The Bat- 
tle of Lake Regillus, ,, when they won the fight for Rome. They were 
regarded as the special patrons of the sailor, who relied much on 
their protection against the evil powers of Orion and the Hyades. 

48. Canis Minor, the Little Dog (Map III.). March. — 
This constellation, about 20° south of Castor and Pollux, is 
marked by the bright star Procyon, which means " before the 
dog," because it rises about half an hour before the Dog 
Star, Sirius. Alpha, Beta, and Gamma form together a config- 
uration closely resembling that formed by Alpha, Beta, and 
Gamma Arietis. Procyon, Alpha Orionis, and Sirius form 
nearly an equilateral triangle, with sides of about 25°. 



38 CANIS MAJOR. [§49 

The animal is supposed to have been one of Orion's dogs, though 
some say the dog of Icarus, whom they identify with Bootes. 

49. Canis Major, the Great Dog (Map II.). February. — 
This glorious constellation hardly needs description. Its 
Alpha is the Dog Star, Sirius 9 beyond all comparison the 
brightest star in the heavens, and one of our nearer neigh- 
bors, — so distant, however, that it requires more than eight 
years for light to come to us from it. It is nearly pointed at 
by a line drawn through the three stars of Orion's belt. Beta, 
at the extremity of the uplifted paw, is of the second magni- 
tude, and so are several of the stars farther south in the rump 
and tail of the animal, who sits up watching his master Orion, 
but with an eye out for Lepus. 

50. Monoceros, the Unicorn (Map II.). March. — This is one 
of the modern constellations organized by Hevelius to fill the gap 
between Gemini and Canis Minor on the north, and Argo Navis and 
Canis Major on the south. It lies just east of Orion, and has no con- 
spicuous stars, but is traversed by a brilliant portion of the Milky 
Way. The Alpha of the constellation (fourth magnitude) lies about 
half-way between Alpha Orionis and Sirius, a little west of the line 
that joins them. 11 Monocerotis, a fine triple star (see Fig. 76, Art. 
366), fourth magnitude, is very nearly pointed at by a line drawn from 
Zeta Canis Majoris northward through Beta, and continued as far 
again. 

51. Argo Navis, the Ship Argo (genitive Argus) (Maps 
II. and III.). March. — This is one of the largest, oldest, and 
most important of the constellations, lying south and east of 
Canis Major. Its brightest star, Alpha Argus, Canopus, ranks 
next to Sirius, and is visible in the Southern States, but not 
in the Northern. The constellation, huge as it is, is only a 
half one, like Pegasus and Taurus, — only the stern of a ves- 
sel, with mast, sail, and oars : the stem being wanting. In the 
part of the constellation covered by our maps there are no 
very conspicuous stars, though there are some of third and 



§ 51] CANCER — LEO. 39 

fourth magnitude which lie east and southeast of the rump 
and tail of Canis Major. We have already mentioned Zeta, or 
Naos, at the southeast extremity of the " Egyptian X." 

According to the Greek legends, this is the miraculous ship in 
which Jason and his fifty companions sailed from Greece to Colchis 
to recover the Golden Fleece. It had in its bow a piece of oak from 
the sacred grove of Dodona, which enabled the ship to talk with its 
commander and give him advice. 

Some see in the constellation the ark of Noah. 

52. Cancer, the Crab (Maps II. and III.) March. — This 
is the fifth of the zodiacal constellations, lying just east of 
Canis Minor. It does not contain a single conspicuous star, 
but is easily recognizable from its position, and in a dark night 
by the nebulous cloud known as Prcesepe, or the "Manger," 
with the two stars Gamma and Delta near it, — the so-called 
Aselli, or " Donkeys." Prsesepe, sometimes also called the 
"Beehive," is really a coarse cluster of seventh and eighth 
magnitude stars, resolvable by an opera-glass. The line from 
Castor through Pollux, produced about 12°, passes near enough 
to it to serve as a pointer. 

The star Zeta is a very pretty triple star, though with a small tel- 
escope it can be seen only as double. It is easily found by a line 
from Castor through Pollux, produced 2\ times as far. 

By the Greeks this was identified as the Crab who attacked Hercu- 
les when he was fighting the Lernsean Hydra. In the old Egyptian 
zodiacs the Crab is replaced by the ScarabaBus, or Beetle ; and in some 
of the more recent zodiacs by a pair of asses, still recognized in the 
name, Aselli, given to the two stars Gamma and Delta. 

53. Leo, the Lion (Map III.). April. — East of Cancer 
lies the noble constellation of Leo, which adorns the evening 
sky in March and April ; it is the sixth of the zodiacal constel- 
lations, now occupying the sign of Virgo. Its leading star, 
Regulus, or "Cor Leonis," is of the first magnitude, and two 
others, Beta (Denebola) and Gamma, are of the second mag- 



40 HYDRA. [§ 53 

nitude. Alpha, Gamma, Delta, and Beta form a conspicuous 
irregular quadrilateral (see map), the line from Eegulus to 
Denebola being about 26° long. Another characteristic con- 
figuration is " the Sickle," of which Eegulus is the handle, 
and the curved line Eta, Gamma, Zeta, Mu, and Epsilon, is the 
blade, the cutting edge being turned towards Cancer. 

The "radiant" of the November meteors lies between Zeta and 
Epsilon. Gamma, in the Sickle, and at the southeast corner of the 
quadrilateral, is a very pretty double star, binary, with a period of 
about 400 years. 

According to classic writers, this is the Nemsean Lion which was 
killed by Hercules, as the first of his Twelve Labors ; but, like Aries 
and Taurus, the constellation is far olde*r than the Greeks, and stands 
in its present form on all the ancient zodiacs. 

54. Leo Minor and Sextans (Map II.) . April. — Leo Minor, 
the Smaller Lion, is an insignificant modern constellation composed of 
a few small stars north of Leo, between it and the feet of Ursa Major. 
It contains nothing deserving special notice. The same remark holds 
good as to Sextans, the Sextant, and even more emphatically. 

55. Hydra (Map III.). March to June. — This constellation, 
with its riders, Crater (the Cup) and Corvus (the Raven), is a 
large and important one, though not very brilliant. The head 
is marked by a group of five or six fourth and fifth magnitude 
stars just 15° south of Praesepe. A curving line of small stars 
leads down southeast to Alpha, Cor Hydrce, or Alphard, a 2\ 
magnitude star standing very much alone. Erom there, as 
the map shows, an irregular line of fourth-magnitude stars 
running far south and then east, almost to the boundary of 
Scorpio, marks the creature's body and tail, the whole cover- 
ing almost six hours of right ascension, and very nearly 90° 
of the sky. About the middle of the length of Hydra, and 
just below the hind feet of Leo (30° due south from Denebola), 
we find the little constellation of Crater ; and just east of it 
the still smaller but much more conspicuous one of Corvus, 



§ 55] VIRGO. 41 

with, two second-magnitude stars in it, and four of the third 
and fourth magnitudes. It is well marked by a characteristic 
quadrilateral (see map), with Delta and Eta together at its 
northeast corner. The order of the letters in Corvus differs 
widely from that of brightness, suggesting that changes may 
have occurred since the letters were applied. 

Epsilon Hydrse and Delta Corvi are pretty double stars, the latter 
easily seen with a small telescope ; colors, yellow and purple. 

Hydra, according to the Greeks, is the immense ^hundred-headed 
monster which inhabited the Lernsean Marsh, and was killed by Her- 
cules as his second labor. But the Hydra of the heavens has only one 
head, and is probably much older than the legends of Hercules. 

An old legend says that Corvus is Coronis, a nymph who was trans- 
formed into a raven to escape the pursuit of Neptune. Another story 
is that she was changed into a crow for telling tales of some impru- 
dent actions that came under her notice. 

56. Virgo (Map III.). May. — East and south of Leo lies 
Virgo, the seventh zodiacal constellation, mostly in the sign 
of Libra. Its Alpha, Spica Virginis, is of the 1± magnitude, 
and, standing rather alone, 10° south of the celestial equator, 
is easily recognized as the southern apex of a nearly equilat- 
eral triangle which it forms with Denebola (Beta Leouis) to 
the northwest, and Arcturus northeast of it. Beta Virginis, of 
the third magnitude, is 14° south of Denebola. A line drawn 
eastward and a little south from Beta (third magnitude) and 
then carried on, curving northward, passes successively (see 
map) through Eta, Gamma, Delta, and Epsilon, of the third 
magnitude. (Notice the word Begde, like Bagdei in Cassio- 
peia, Art. 28.) 

Gamma is a remarkable binary star, at present easily visible as 
double in a small telescope. Its period is one hundred and eighty-five 
years, and it has completed pretty nearly a full revolution since its 
first discovery. For a diagram of its orbit, see Fig. 77, Art. 369. A 
few degrees north of Gamma lies the remarkable nebulous region of 



42 CANES VENATICI. [§ 56 

Virgo, containing hundreds of these curious objects ; but for the most 
part they are very faint, and observable only with large telescopes. 

The classic poets recognize Virgo as Astrsea, the goddess of justice, 
■who, last of all the old divinities, left the earth at the close of the 
Golden Age. She holds the Scales of Justice (Libra) in one hand, 
and in the other a sheaf of wheat. 

Some identify her with Erigone, the daughter of Icarus or Bootes. 
Others recognize in her the Egyptian Isis. 

57. Coma Berenices, Berenice's Hair (Map III.). May. — This 
little constellation, composed of a great number of fifth and sixth 
magnitude stars, lies 30° north of Gamma and Eta Virginis, and about 
15° northeast of Denebola. It contains a number of interesting 
double stars, but they are not easily found without the help of a tele- 
scope equatorially mounted. 

The constellation was established by the Alexandrian astronomer 
Con on, in honor of the queen of Ptolemy Soter. She dedicated her 
splendid hair to the gods, to secure her husband's safety in war. 

58. Canes Venatici, the Hunting-Dogs (Map III.). May. — 

These are the dogs with which Bootes, the huntsman, is pursu- 
ing the Great Bear around the pole : the northern of the two 
is Asterion, the southern Char a. Most of the stars are small, 
but Alpha is of the 2\ magnitude, and is easily found by draw- 
ing from Eta Ursse Majoris (the star in the end of the Dipper- 
handle) a line to the southwest, perpendicular to the line from 
Eta to Zeta (Mizar), and about 15° long : in England it is gen- 
erally known as Cor Caroli (the Heart of Charles), in allusion 
to Charles I. With Arcturus and Denebola it forms a triangle 
much like that which, they form with Spica. 

The remarkable whirlpool nebula of Lord Rosse is situated in this 
constellation, about 3° west and somewhat south of the star Eta Ursse 
Majoris. In a small telescope it is by no means conspicuous, but in a 
large telescope is a wonderful object. 

The constellation is modern, formed by Hevelius. 

59. Bootes, the Huntsman (Maps I. and III.). June. — This 
fine constellation extends more than 60° in declination, from 






§ 59 J CORONA BOKEALIS. 43 

near the equator quite to Draco, where the uplifted hand hold- 
ing the leash of the hunting-dogs overlaps the tail of the Bear. 
Its principal star; Alpha, Arcturus (meaning ( bear-driver '), is 
of a ruddy hue, and in brightness is excelled only by Sirius 
among the stars visible in our latitudes. It is at once recog- 
nizable by its forming with Spica and Denebola the great tri- 
angle already mentioned (Art. 56). Six degrees west and a 
little south of it is Eta, of the third magnitude, which forms 
with it, in connection with Upsilon, a configuration like that 
in the head of Aries. Epsilon is about 10° northeast of Arc- 
turus, and in the same direction about 10° farther lies Delta. 
The word Bootes means " the shouter," — the huntsman call- 
ing to his dogs. 

Epsilon is a fine double star ; colors, orange and greenish blue ; 
distance, about 3". 

The legendary history of this constellation is very confused. One 
legend makes it to be Icarus, the father of Erigone (Virgo). But the 
one most usually accepted makes it to be Areas, son of Callisto. After 
she was changed to a bear (Ursa Major), her son, not recognizing her, 
hunted her with his dogs, and was on the point of killing her, when 
Jupiter interfered and took them both to the stars. 

60. Corona Borealis, the Northern Crown (Map III.). June. 
— This beautiful little constellation lies 20° northeast of Arc- 
turus, and is at once recognizable as an almost perfect semi- 
circle composed of half a dozen stars, among which the bright- 
est, Alpha (Gemma or Alphacca), is of the second magnitude. 
The extreme northern one is Theta ; next comes Beta, and the 
rest follow in the Bagdei order, just as in Cassiopeia. About a 
degree north of Delta 5 now visible with an opera-glass, is a 
small star which in 1866 suddenly blazed out until it became 
brighter than Alphacca itself (see Art. 355). 

The little star Eta is a rapid binary with a period of less than forty 
two years. At times it can be easily divided by a small telescope. 

The constellation is said to be the crown that Bacchus gave to 
Ariadne, before he deserted her on the island of Naxos. 



44 LIBRA — CENTATJBUS. [§ 61 

61. Libra, the Balance (Map III.). June. — This is the 
eighth of the zodiacal constellations, lying east of Virgo, 
bounded on the south by Centaurus and Lupus, on the east by 
the upstretched claw of Scorpio, and on the north by Serpens 
and Virgo. It is inconspicuous, the most characteristic figure 
being the trapezoid formed by the lines joining the stars Alpha, 
Iota, Gamma, and Beta. Beta, which is the northern one, is 
about 30° due east from Spica, while Alpha is about 10° south- 
west of Beta. The remarkable variable, Delta Librae, is 4° 
west and a little north from Beta. Most of the time it is of 
the 4|- or 5 magnitude, but runs down nearly two magnitudes, 
to invisibility, once in 2\ days. "Algol" type (Art. 358). 

Libra is the Balance of Virgo, the goddess of justice, and was not 
recognized by the classic writers as a separate constellation until the 
time of Julius Csesar ; the space now occupied by Libra being then 
covered by the extended claws of Scorpio. 

62. Antlia, Centaurus, and Lupus (Map III.). April to 
June. — These constellations lie south of Hydra and Libra. 

Antlia Pneumatica (the Air-Pump) is a modern constellation of no 
importance and hardly recognizable by the eye, having Only a single 
star as bright as the 4.] magnitude. 

Centaurus, on the other hand, is an ancient and extensive 
asterism, containing in its south (circumpolar) regions, not 
visible in the United States, two stars of the first magnitude, 
Alpha and Beta. Alpha Centauri stands next after Sirius and 
Canopus in brightness, and, as far as present knowledge indi- 
cates, is our nearest neighbor among the stars. The part of the 
constellation which becomes visible in our latitudes is not 
especially brilliant, though it contains several stars of the 2\ 
and 3 magnitudes in the region lying south of Corvus and 
Spica Virginis. 

Lupus, the Wolf, also one of Ptolemy's constellations, lies due east 
of Centaurus and just south of Libra. It contains a considerable 



§ 62] SCORPIO. 45 

number of third and fourth magnitude stars ; but it is too low for 
any satisfactory study in our latitudes. It is best seen late in June. 
These constellations contain numerous objects interesting for a south- 
ern observer, but not observable by us. 

The Centaurs were a fabulous race, half man, half horse, who lived 
in Thessaly and herded cattle. Chiron was the most distinguished of 
them, the teacher of almost all the Greek heroes in every manly and 
noble art, and the friend of Hercules, by whom, however, he was acci- 
dentally killed. Jupiter transferred him to the stars. (See Sagitta- 
rius, Art. 72.) The wolf is represented as transfixed by the Centaur's 
spear. 

63. Scorpio (or Scorpius; genitive Scorpii), the Scorpion 
(Map IV.). July. — This, the ninth of the zodiacal constel- 
lations and the most brilliant of them all, lies southeast of 
Libra, which in ancient times used to form its claws (Chelae). 
It is recognized at once by the peculiar configuration of the 
stars, which resembles a boy's kite, with a long streaming tail 
extending far down to the south and east, and containing sev- 
eral pairs of stars. The principal star of the constellation, 
Antares, is of the first magnitude, and fiery red like the planet 
Mars. From this it gets its name, which means "the rival 
of Ares" (Mars). Antares is a very pretty double star, with 
a beautiful little green companion just to the west of it, not 
very easy to be seen, however, with a small telescope. Beta 
(second magnitude) is in the arch of the kite bow, about 8° or 
9° northwest of Antares, while the star which Bayer lettered 
as Gamma Scorpii is well within Libra, 20° west of Antares. 
(There is considerable confusion among uranographers as to 
the boundary between the two constellations.) The other 
principal stars of the constellation are easily found on the 
map. 

Many of them are of the second magnitude. One of the finest 
clusters known, and easily seen with a small telescope, is Messier 80, 
which lies about half-way between Alpha and Beta. 

According to the Greek mythology, this is the scorpion that killed 



46 OPHIUCHUS AND SERPENS. [§ 63 

Orion. It was the sight of this monster of the heavens that frightened 
the horses of the sun, when poor Phaeton tried to drive them and was 
thrown out of his chariot. Among astrologers, the influence of Scorpio 
has always been held as baleful to the last degree. 

64. Norma Nilotica, the rule with which the height of the Nile 
was measured, lies west of Scorpio, while Ara lies due south of Eta 
and Theta. Both are old Ptolemaic constellations, but are small and 
of little importance, at least to observers in our latitudes. 

65. Ophiuchus and Serpens (Maps III. and IV). July. — Ophi- 
uchus means " serpent-holder," and probably refers to the great 
physician, iEsculapius. The hero is represented as standing 
with his feet on Scorpio, and grasping the " serpent." The 
two constellations, therefore, are best treated together. The 
head of Serpens is marked by a group of small stars lying just 
south of Corona and 20° due east of Arcturus. Beta and 
Gamma are the two brightest stars in the group, their magni- 
tudes 3J and 4. Delta lies 6° southwest of Beta, and there 
the Serpent's body bends southeast through Alpha and Epsilon 
Serpentis (see map) to Delta and Epsilon Ophiuchi in the 
giant's hand. The line of these five stars carried upwards 
passes nearly through Epsilon Bootis, and downwards through 
Zeta Ophiuchi. A line crossing this at right angles, nearly 
midway between Epsilon Serpentis and Delta Ophiuchi, passes 
through Mu Serpentis on the southwest and Lambda Ophiuchi 
to the northeast. The lozenge-shaped figure formed by the 
lines drawn from Alpha Serpentis and Zeta Ophiuchi to the 
two stars last mentioned is one of the most characteristic 
configurations of the summer sky. Alpha Ophiuchi (2^- mag- 
nitude) (Ras Alagliue) is easily recognizable in connection 
with Alpha Herculis, since they stand rather isolated, about 6° 
apart, on the line drawn from Arcturus through the head of 
Serpens, and produced as far again. Alpha Ophiuchi is the 
eastern and the brighter of the two, and forms with Vega and 
Altair a nearly equilateral triangle. Beta Ophiuchi lies about 
9° southeast of Alpha. 



§ 65] HERCULES. 47 

Five degrees east and a little south of Beta are five small stars in 
the Milky Way, forming a V with the point to the south, much like 
the Hyades of Taurus. They form the head of the now discredited 
constellation, " Poniatowski's Bull" (Taurus Poniatouii), proposed in 
1777, and found in many maps. 70 Ophiuchi (the middle star in the 
eastern leg of the V of Poniatowski's Bull) is a very pretty double star, 
binary, with a period of ninety-three years. Just at present the star 
is too close to be resolved by a small instrument, but it will soon open 
up again. 

Ophiuchus is identified with JEsculapius, who was the first great 
physician, the son of Apollo and the nymph Coronis, educated in the 
art of medicine by Chiron, the Centaur. The serpent and the cock 
were sacred to him in his character as a deity. But the constellation 
is older than the classic legends. 

66. Hercules (Maps III. and IV.). July. — This noble con- 
stellation lies next north of Ophiuchus, between it and Draco. 
The hero is represented as resting on one knee, with his foot 
on the head of Draco, while his head is close to that of Ophiu- 
chus. The constellation contains no stars of the first or even 
of the second magnitude, but there are a number of the third. 
The most characteristic figure is the keystone-shaped quadri- 
lateral formed by the stars Epsilon, Zeta, Eta, with Pi and 
Eho together at the northeast corner. It lies about midway 
on the line from Vega to Corona. 

On its western boundary, a third of the way from Eta towards Zeta, 
lies the remarkable cluster, Messier 13, — on the whole the finest of 
all star clusters, — barely visible to the naked eye on a dark night. 
Alpha Herculis (Ras Algethi), in the head of the giant, is a very 
beautiful double star, colors orange and blue, distance about 5". It 
is slightly variable, and has a remarkable spectrum, characterized by 
numerous dark bands. 

Hercules, the son of Jupiter and Alcmena (a granddaughter of 
Andromeda), was the Greek incarnation of gigantic strength. His 
heroic actions and freaks occupy more space in their mythology than 
those of any personage except Jupiter himself. He was the pupil of 
Chiron, but by the will of Jupiter, his father, was subjected to the 



48 LYRA — CYGNUS. L§ ^ 

power of Eurystheus, the king of Tiryns, for many years. At his 
bidding he performed the great enterprises known as the Twelve 
Labors of Hercules, for which we must refer the reader to the Classi- 
cal Dictionaries. Among them we have already mentioned the con- 
quest of the Nemsean Lion and of the Lernsean Hydra. Another was 
to bring from the garden of the Hesperides the golden apples which 
were guarded by the dragon that he killed, and on which his feet rest 
in the sky. His last and greatest achievement was to bring to the 
earth the three-headed dog, Cerberus, the guardian of the infernal 
regions. 

67. Lyra (Map IV.). August. — This constellation is suffi- 
ciently marked by the great white or blue star, Vega, one of 
the finest stars in the whole sky, and certainly many times 
larger than our own sun. It is attended on the east by two 
fourth-magnitude stars, Epsilon and Zeta, which form with it 
a little equilateral triangle having sides about 2° long. Epsi- 
lon is a double-double or quadruple star. A sharp eye, even 
unaided by a telescope, divides the star into two, and a large 
telescope splits each of the components. It is a very pretty 
object even for a small telescope (Fig. 76). Beta and Gamma, 
of the third magnitude (Beta is variable), lie about 8° south- 
east from Vega, 2£° apart. (See Art. 357.) 

On the line between Beta and Gamma, one-third of the way from 
Beta, lies Messier 57, the Annular Nebula, which can be seen as a 
small hazy ring even by a small telescope, though of course it is much 
more interesting with a larger one. 

According to the legends this constellation is the lyre of Orpheus, 
with which he charmed the stern gods of the lower world, and per- 
suaded them to restore to him his lost Eurydice. 

68. Cygnus (Maps I. and IV.). September. — This con- 
stellation lies due east from Lyra, and is easily recognized by 
the cross that marks it. The bright star Alpha (1^- magni- 
tude) is at the top, and Beta (third magnitude) at the bottom, 
while Gamma is where the cross-bar from Delta to Epsilon 
intersects the main piece, which, lies along the Milky Way 



§ 68] VTTLPECULA ET ANSER. 49 

from the northeast to the southwest. Beta (Albireo) is a 
beautiful double star, orange and dark blue, one of the finest 
of the colored pairs for a small telescope. 61 Cygni, which is 
memorable as the first star to have its parallax determined (by 
Bessel in 1838), is easily found by completing the parallelo- 
gram of which Alpha, Gamma, and Epsilon are the other three 
corners. Sigma and Tau form a little triangle with 61, which 
is the faintest of the three. 61 is a fine double star. Delta 
is also a fine double, but too difficult for an instrument of less 
than six inches' aperture. 

According to Ovid, Cygnus was a friend of Phaeton's, who mourned 
his unhappy fate and was changed to a swan. Others see in the con- 
stellation the swan in whose form Jupiter visited Leda, the mother of 
Castor and Pollux and of Helen of Troy. 

69. Vulpecula et Anser, the Fox and the Goose (Map IV.). 
September. — This little constellation is one of those originated by 
Hevelius, and has obtained more general recognition among astrono- 
mers than most of his creations. It lies just south of Cygnus, and is 
bounded to the south by Delphinus, Sagitta, and Aquila. It has no 
conspicuous stars, but it contains one very interesting telescopic 
object, — the " Dumb-bell Nebula " (see map). It may be found on a 
line from Gamma Lyrse through Beta Cygni, produced as far again. 

70. Sagitta (Map IV.). August. — This little constellation, though 
very inconspicuous, is one of the old 48. It lies south of Vulpecula, 
and the two stars Alpha and Beta, which mark the feather of the 
arrow, lie nearly midway between Beta Cygni and Altair, while its 
point is marked by Gamma, 5° farther east and north. Beta, the 
middle star of the shaft of the arrow, is a very pretty double star, dis- 
tance about 8" : the larger star is itself a close double. 

71. A'quila (not A-qui'la) (Map IV.). August. —This 
constellation lies on the celestial equator, east of Ophiuchus 
and north of Sagittarius and Capricornus. Its characteristic 
configuration is that formed by Alpha, Altair, with Gamma to 
the north and Beta to the south. It lies about 20° south of Beta 



50 SAGITTARIUS. [§ 71 

Cygni, and forms a fine triangle with Beta and Alpha Ophiu- 
chi. Altair is taken as the standard first-magnitude star. Of 
course, several of those which are called first magnitude, like 
Sirius and Vega, are very much brighter than this, while others 
fall considerably below it. 

Aquila was the bird of Jupiter, which he kept by the side of his 
throne and sent to bring Ganymede to him. 

The southern part of the region allotted to Aquila on our maps has 
been assigned to Antinoiis, which is recognized on some celestial 
globes. The constellation existed even in Ptolemy's time, but he 
declined to adopt it. Hevelius has appropriated the eastern part of 
Antinoiis for his constellation of Scutum Sobieski. 

72. Sagittarius, the Archer (Map IV.). August. — This, 
the tenth of the zodiacal constellations, contains no stars of the 
first magnitude, but a number of the second and third magni- 
tude, which make it reasonably conspicuous. The most char- 
acteristic configuration is the little inverted " milk-dipper," 
formed by the five stars, Lambda, Phi, Sigma, Tau, and Zeta, 
of which the last four form the bowl, while Lambda (in the 
Milky Way) is the handle (see map). Delta, Gamma, and 
Epsilon, which form a triangle, right-angled at Delta, lie south 
and a little west of Lambda, the whole eight together forming 
a very striking group. There is a curious disregard of any 
apparent principle in the lettering of the stars of this con- 
stellation ; Alpha and Beta are stars not exceeding in bright- 
ness the fourth magnitude, about 4° apart on a north and south 
line, and lying some 15° south and 5° east of Zeta (see map), 
while Sigma is now a bright second-magnitude star, strongly 
suspected of being irregularly variable. (The constellation 
contains an unusual number of known variables.) The Milky 
Way in Sagittarius is very bright and complicated in structure, 
full of knots and streamers and dark pockets, and containing 
many beautiful and interesting objects. 

This con.3t.ellation is said by many writers to commemorate the 
Centaur, Chiron, but the same constellation appears on the ancient 



§ 72 J CAPRICORNUS — DELPHINUS. 51 

zodiacs of Egypt and India, and it seems probable, therefore, that, 
like the Bull and the Lion, it was not representative of any particular 
individual. 

73. Capricornus (Map IV.). September. — This, the eleventh 
of the zodiacal constellations, follows Sagittarius on the east. 
It has no bright stars, but the configuration formed, by the two 
Alphas (ax and a 2 ) with each other and with Beta, 3° south, is 
characteristic, and not easily mistaken for anything else. The 
two Alphas, a pretty double to the naked eye, lie on the line 
drawn from Beta Cygni (at the foot of the cross) through 
Altair, and produced about 25°. 

Some say that this constellation represents the god Pan, who was 
represented by the Greeks as having the legs of a goat and the head of 
a man. Others find in the goat, Amalthea (the foster-mother of the 
infant Jupiter), who is also, it will be remembered, represented in the 
constellation of Auriga. 

74. Delphinus, the Dolphin (Map IV.). September. — This 
constellation, though small, is one of the ancient 48, and is 
unmistakably characterized by the rhombus of third-magnitude 
stars known as " Job's Coffin." It lies about 15° east of Altair. 
There are a few stars visible to the naked eye, in addition to 
the four that form the rhombus. Epsilon, about 3° to the 
southwest, is the only conspicuous one. 

Gamma, at the northwest angle of the rhombus, is a very pretty 
double star. Beta is also a very close and rapid binary, beyond the 
reach of all but large telescopes. 

This is the Dolphin that preserved the life of the musician, Arion, 
who was thrown into the sea by sailors, but carried safely to land 
upon the back of the compassionate fish, who loved his music. 

75. Equuleus, the Little Horse (Map IV.). This little con- 
stellation, simply a horse's head, though still smaller than the Dolphin 
and less conspicuous, is also one of Ptolemy's. It lies about 20° due 
east of Altair, and 10° southeast of the Dolphin (see map). 



52 PEGASUS — AQUARIUS. [§ 7 ^ 

76. Lacerta, the Lizard (Maps I. and IV.). This is one of 
Hevelius's modern constellations, lying between Cygnus and Androm- 
eda, with no stars above the 4J magnitude, and of no importance for 
our purposes. 

77. Pe'gasus (not Pe-gas'us) (Map IV.). October. — This 
winged horse covers an inmiense space. Its most notable con- 
figuration is the " great square/ 5 formed by the second-mag- 
nitude stars, Alpha (Markab), Beta, and Gamma Pegasi, in 
connection with Alpha Andromedse (sometimes lettered Delta 
Pegasi), at its northeast corner. The stars of the square lie in 
the body of the horse, which has no hindquarters. A line drawn 
from Alpha Andromedae through Alpha Pegasi, and produced 
about an equal distance, passes through Xi and Zeta in the 
animal's neck, and reaches Theta in his ear. Epsilon (or 
Enif), the bright star 8° northwest of Theta, marks his nose. 
The forelegs are in the northwestern part of the constellation 
just east of Cygnus, and are marked, one of them by the stars 
Eta and Pi, and the other by Iota and Kappa. 

This is the winged horse which sprang from the blood of Medusa, 
after Perseus had cut off her head. He fixed his residence on Mt. 
Helicon, where he was the favorite of the Muses, and after being 
tamed by Minerva he was given to Bellerophon to aid him in conquer- 
ing the Chimera. After the destruction of the monster, Bellerophon 
attempted to ascend to heaven upon Pegasus, but the horse threw off 
his rider, and continued his flight to the stars. 

78. Aquarius, the Water-bearer (Map IV.). October. — 
This, the twelfth and last of the zodiacal constellations, 
extends more than 3|- h in right ascension, covering a con- 
siderable region which by rights ought to belong to Capri- 
cornus. The most notable configuration is the little Y of 
third and fourth magnitude stars which marks the " water- 
jar" from which Aquarius pours the stream that meanders 
down to the southeast and south for 30°, till it reaches the 
Southern Fish. The middle of the Y is about 18° south and 



§ 78] PISCIS AUSTRINUS. 53 

west of Alpha Pegasi, and lies almost exactly on the celestial 
equator. 

Zeta, the central star of the Y, is a pretty and interesting double 
star, distance about -i". The green nebula, nearly on the line from 
Alpha through Beta, produced about its own length, 1J° west of Nu, 
is a planetary nebula, and curious from the vividness of its color (see 
map). 

There are various opinions respecting the origin of this constella- 
tion. According to a Greek legend it represents Deucalion, the hero 
of the Greek Deluge ; but among the Egyptians it evidently had refer- 
ence to the rising and falling of the Nile. 

79. Piscis Austrinus (or Australis), the Southern Fish (Map 
IV.). October. — This small constellation, lying south of Cap- 
ricornus and Aquarius in the stream that issues from the 
Water-bearer's urn, presents little of interest. It has one 
bright star, Fomalhaut (pronounced Fomalo), of the 1^- mag- 
nitude, which is easily recognized from its being nearly on the 
same hour-circle with the western edge of the great square of 
Pegasus, 45° to the south of Alpha Pegasi, and solitary, hav- 
ing no star exceeding the fourth magnitude within 15° or 20°. 

This constellation is by some said to represent the transformation 
of Venus into a fish, when fleeing from Typhon (but see Pisces). 

South of the Southern Fish, barely rising above the southern hori- 
zon, lie the constellations of Microscopium and Grus. The former is 
of no account. In the southern hemisphere Grus is a conspicuous 
constellation, and its two brightest stars, Alpha and Beta, of the sec- 
ond magnitude, rise high enough to be seen in latitudes south of 
Washington. They lie about 20° south and west of Fomalhaut. 



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§80] 



LATITUDE DEFINED. 



55 



CHAPTER III. 



LATITUDE, AND THE ASPECT OF THE CELESTIAL SPHERE. 
— TIME. — LONGITUDE. — THE PLACE OF A HEAVENLY 
BODY. 

80. Latitude defined. — In geography the latitude of a place 
is usually defined simply as its distance north or south of the 
equator, measured in degrees. This is not explicit enough, 
unless it is stated how the degrees themselves are to be meas- 
ured. There would be no difficulty if the earth were a perfect 
sphere ; but since the earth is a little flattened at the poles ; 
the degrees (geographical) are of somewhat different lengths 
at different parts of the earth. The exact definition of the 
astronomical latitude of 
a place is the angle be- 
tween the direction of the 
observer's plumb-line and 
the plane of the earth's 
equator ; and this is the 
same as the altitude of 
the pole, as will be clear 
from Tig. 6. Here the 
angle ONQ is the lati- 
tude as defined. If now 
at we draw HH' per- 
pendicular to OZ, it will 
be a level line, and will point to the horizon. Trom also 
draw OP", parallel to CP, the earth's axis. Since OP f and 
CP n are parallel they will be directed apparently to the same 
point in the celestial sphere (Art. 6), and this point is the 




Fig. 6. - 



■Relation of Latitude to the Elevation 
of the Pole. 



56 MEASURING THE LATITUDE. [§ 80 

celestial pole. The angle H'OP" is therefore the altitude of 
the pole, as seen at 0, and it obviously equals ONQ ; and this 
is true whether the earth be a sphere, or whatever its form. 
This fundamental relation, that the altitude of the pole 

IS IDENTICAL WITH THE OBSERVER'S LATITUDE, Cannot be tOO 

strongly impressed on the mind, 

81. Method of measuring the Latitude. — The most obvious 
method is to observe, with a suitable instrument, the altitude 
of some star near the pole (a " circumpolar " star) at the 
moment when it is crossing the meridian above the pole, and 
again twelve hours later, when it is once more on the meridian 
below the pole. In the first position, its elevation is the great- 
est possible ; in the second, the least. The average of these two 
altitudes, when corrected for refraction, is the latitude of the 
observer. It is exceedingly important that the student under- 
stand this simple method of determining the latitude. 

The instrument ordinarily used for making observations of this 
kind at an observatory is called a meridian circle, and a brief descrip- 
tion is given in the Appendix (see Art. 418). 

82. Refraction. — When we observe the altitude of a heav- 
enly body with any instrument, we do not find it as it would 
be if our atmosphere had no effect upon the rays of light. As 
these rays enter the earth's atmosphere they are bent down- 
ward by " ref raction," excepting only such as come from 
exactly overhead. Since the observer sees the object in the 
direction in which the rays enter the eye, without any reference 
to its real position, this bending down of the rays causes every 
object seen through the air to look higher up in the sky than 
it would be if the air were absent; and we must therefore 
correct the observed altitude by diminishing it a certain 
amount. Under ordinary conditions, refraction elevates a 
body at the horizon about 35', so that the sun and moon in 
rising appear clear of the horizon while they are still wholly 



§ 82] THE RIGHT SPHERE. 57 

below it. The refraction correction diminishes very rapidly 
as the body rises. At an altitude of only 5° the refraction is 
but 10'; at 44°, it is about l'j and at the zenith, zero, of 
course. 

Its amount at any given time is affected quite sensibly, however, by 
the temperature and by the height of the barometer, increasing as the 
thermometer falls or as the barometer rises ; so that whenever great 
accuracy is required in measures of altitude we must have observa- 
tions of both the barometer and thermometer to go with the reading 
of the circle. In works on Practical Astronomy tables are given by 
which the refraction can be computed for an object at any altitude 
and in any state of the weather. *[t is hardly necessary to say that 
this indispensable correction is very troublesome, and always involves 
more or less error. 

For other methods of determining the latitude, see Appendix, 
Art. 424. 

83. Effect of the Observer's Latitude upon the Aspect of the 
Heavens ; the Right Sphere. — If the observer is situated at the 
earth's equator, — i.e., in latitude zero, — the celestial poles will 
evidently be on the horizon, and the celestial equator will pass 
through the zenith and coincide with the prime vertical (Art. 
11). At the earth's equator, therefore, all heavenly bodies 
will rise and set vertically, and their diurnal circles will be 
equally divided by the horizon, so that they will be twelve 
hours above it and twelve hours below it, and the length of 
the night will always equal that of the day. This aspect of 
the heavens is called the right sphere. 

84. Parallel Sphere. — If the observer is at one of the poles 
of the earth, where the latitude equals 90°, then the corre- 
sponding celestial pole will be exactly overhead, and the 
celestial equator will coincide with the horizon. If he is at 
the north pole, all the stars north of the celestial equator will 
remain permanently visible, never rising or setting, but sailing 
around the sky on parallels of altitude, while the stars south 



58 



THE OBLIQUE SPHERE. 



[§84 



of the equator will never rise to view. Since the sun and the 
moon move in such a way that during half the time they are 
north of the equator and half the time south of it, they will 
therefore be half the time above the horizon and half the time 
below it (that is, approximately, since refraction has a notice- 
able effect). The moon will be visible for about a fortnight 
at a time, and the sun for about six months. 



85. The Oblique Sphere. — At any station between the pole 
and the equator the pole will be elevated above the horizon, 

and the stars will rise and 
set in oblique circles, as 
shown in Fig. 7. Those 
stars whose distance from 
the elevated pole is less 
than PN, the latitude of 
the observer, will never 
N set, the radius of this "cir- 
cle of perpetual appari- 
tion" being just equal to 
the height of the pole, and 
becoming larger as the lat- 
itude increases. On the 
other hand, stars within 
the same distance of the 
depressed pole will lie within the " circle of perpetual occupa- 
tion," and will never rise above the observer's horizon. An 
object which is exactly on the celestial equator will have its 
diurnal circle, EQWQ f , equally divided by the horizon, and 
will be above the horizon just as long as below it. 

For an observer in the United States, a star north of the 
equator will have more than half of its diurnal circle above the 
horizon, and will be visible for more than twelve hours of each 
day; as, for instance, the star at A. Whenever the sun is 
north of the celestial equator, the day will therefore be longer 




Fig. 7. — The Oblique Sphere. 



§ 85] THE OBLIQUE SPHERE. 59 

than the night for all stations in northern latitude: how 
much longer will depend both on the latitude of the place and 
the sun's distance from the equator (its declination). 

86. Moreover, when the sun is north of the equator, it will, 
in the northern latitudes, rise at a point north of east, as at B 
in the figure, and will continue to shine on the north side of 
every wall that runs east and west until, as it ascends, it 
crosses the prime vertical, EZW, at some point, as V. In the 
latitude of New York the sun in June is south of the prime 
vertical for only about six hours of the whole fifteen during 
which it is above the horizon. During nine hours of the day, 
therefore, it shines into north windows. 

If the latitude of the observer is such that PN, in the figure, 
is greater than the sun's polar distance at the time when it is 
farthest north, the sun at midsummer will make a complete 
circuit of the heavens without setting, thus producing the 
phenomenon of the " midnight sun," visible at the North Cape 
and at all stations within the Arctic Circle. 

87. A celestial globe will be of great use in studying these 
diurnal phenomena. The north pole of the globe must be 
elevated to an angle equal to the latitude of the observer, 
which can be done by means of the degrees marked on the 
metal meridian ring. It will then be seen at once what stars 
never set, which ones never rise, and during what part of the 
twenty-four hours any heavenly body at a known distance 
from the equator is above or below the horizon. For descrip- 
tion of the celestial globe, see Appendix, Art. 400. 

TIME. 

Time is usually defined as "measured duration," and the 
standard unit of time has always been obtained in some way 
from the length of the day. 



60 SOLAR TIME. [§ 88 

88. Apparent Solar Time. — The most natural way, since 
we are obliged to regulate our lives by the sun, is to reckon 
time by him ; i.e., to call it noon when the sun is on the merid- 
ian and highest, and to divide the day from one noon to 
another into its hours, minutes, and seconds. Time thus 
reckoned is called apparent solar time (see Appendix, Art. 
422), which is the time shown by a correctly adjusted sun- 
dial. But because the sun's eastward motion in the sky is 
not uniform (owing to the oval form of the earth's orbit, and 
its inclination to the equator), these apparent solar days are not 
exactly of the same length. Thus, for instance, the interval 
from noon of Dec. 22d to noon of Dec. 23d is nearly a minute 
longer than the interval between the noons of Sept. 15th and 
16th. As a consequence, it is only by very complicated and 
expensive machinery that a watch or clock can be made to 
keep time precisely with the sundial, and the attempt was 
long ago given up. Apparent solar time is now used only in 
communities where clocks and watches are rare, and sundials 
are the usual timepieces. 

89. Mean Solar Time. — At present, for civil and business 
purposes, time is almost universally reckoned in days all of 
which have precisely the same length, and are just equal to 
the average apparent solar day ; and this time, called mean 
solar time (Appendix, Art. 422), is that which is kept by all 
good timepieces. 

Sundial time agrees -with mean time four times a year; viz., upon 
April 15th, June 14th, Sept. 1st, and Dec. 24th. The greatest differ- 
ences occur on Nov. 2d and Feb. 11th, when the sundial is respec- 
tively 16 m 20 8 fast of the clock and 14 m 30" slow. During the summer 
the difference never exceeds 6 m . This difference is called the Equation 
of Time, and is given in the almanac for every day in the year. 

90. The Civil Day and the Astronomical Day. — The astro- 
nomical day begins at noon ; the civil day at midnight, twelve hours 
earlier. Astronomical mean time is reckoned around through the 



§ 90] SIDEREAL TIME. 61 

whole twenty-four hours, instead of being counted in two series of 
twelve hours each. Thus 8 a.m. of Tuesday, Aug. 12th, civil reck 
oning, is Monday, Aug. 11th, 20\ astronomical reckoning. Beginners 
need to bear this in mind in referring to the almanac. 

91. Sidereal Time, or Time reckoned by the Stars. — As has 
been said (Art. 17), the sun is not fixed on the celestial sphere, 
but appears to creep completely around it once a year. The 
interval from noon to noon does not therefore correspond to 
the true diurnal revolution of the heavens. If we reckoned by 
the interval between two successive passages of any given 
star across the observer's meridian, we should find that the 
true day, the sidereal day, as it is called, is nearly 4 m shorter 
(3 m 56 s .9) than the ordinary solar day; the relation being such 
that in a year the number of sidereal days exceeds that of solar 
by exactly one. For many purposes, astronomers find it much 
more convenient to reckon by the stars than by the sun. 
They count the time, however, not by any real star, but from 
the Vernal Equinox, the sidereal clock being so set and regu- 
lated that it always shows zero hours, minutes, and seconds, 
at the moment when the Vernal Equinox is on the meridian 
(see Appendix, Art. 422). Sidereal time, of course, would 
not answer for business purposes, since its noon comes at all 
hours of the day and night at different seasons of the year. 
The almanac gives data by which sidereal time and mean solar 
time can be easily converted into each other. 

92. The Determination of Time. — In practice, the problem 
always takes the shape of finding the error of a timepiece of 
some sort; i.e., ascertaining how many seconds it is fast or 
slow. The instrument now ordinarily used for the purpose is 
the transit instrument, which is a small telescope mounted on 
an axis, placed exactly east and west, and level, so that as the 
telescope is turned it will follow the meridian ; at least, the 
middle cross-wire in the field of view will do so. It is the 



62 TIME FROM THE STARS. [§ 92 

same as the meridian circle, except that it does not require 
the costly graduated circle with its appendages. For descrip- 
tion, see Appendix, Art. 416. 

To determine with the transit the error of the sidereal clock 
which is ordinarily used in connection with it, it is only neces- 
sary to observe the exact time indicated by the clock when 
some star whose right ascension is known passes, or " tran- 
sits," the middle wire of the instrument. 

93. The right ascension of a star (Art. 18) is the number of 
< hours ? of arc (measured along the equator) by which the star 
is east of the vernal equinox ; and therefore when the star is 
on the meridian, the right ascension also equals the number 
of hours, minutes, and seconds since the transit of the vernal 
equinox. In other words, we may say that the right ascension 
of a star is the sidereal time at the moment of its meridian tran- 
sit (This is often called the observatory definition of right 
ascension.) For instance, the right ascension of Vega (Alpha 
Lyrse) is 18 h 33 m . If we observe its transit to occur at 18 h 40 m 
by the clock, the clock is obviously 7 m fast. 

With a good instrument, a skilled observer can thus deter- 
mine the clock-error within about -^ of a second of time. 

To get solar time, we may observe the sun itself, the moment 
of its transit being c apparent noon.' But it is better, and it 
is usual, to get the sidereal time first, and to deduce from that 
the solar time by means of the necessary data which are fur- 
nished in the almanac. 

The method by the transit instrument is most used, and is, on the 
whole, the most convenient ; but since the instrument requires to be 
mounted upon a firm pier, it is not always available. When not, we 
use some one of various other methods, for which reference must be 
made to the General Astronomy. At sea, and by travellers on scien- 
tific expeditions, the time is usually determined by observing the alti- 
tude of the sun with a sextant some hours before or after noon. (See 
Appendix, Art. 427.) 



§ 94] DETERMINATION OF LONGITUDE. 63 

LONGITUDE. 

94. The problem of rinding the longitude is in many respects 
the most important of what may be called the " economic" 
problems of astronomy ; i.e., those of business utility to man- 
kind. The great observatories of Greenwich and Paris were 
founded for the express purpose of furnishing the necessary 
data to enable the sailor to determine his longitude at sea; 
and the English government has given great prizes for the 
construction of clocks and chronometers fit to be used in such 
determinations. 

The longitude of a place on the earth is defined as the 
arc of the equator intercepted between the meridian which passes 
through the place and some meridian ivhich is taken as the 
standard. 1 

Now since the earth turns on its axis at a uniform rate, this 
arc is strictly proportional to, and may be measured by, the 
time intervening between the transits of any given star across 
the two meridians. The longitude of a place may therefore 
be defined as the amount by ivhich the time at Greenwich is ear- 
lier or later than the time at the station of the observer; and this 
whether we reckon by solar or by sidereal time. Accordingly, 
terrestrial longitude is usually reckoned in hours, minutes) 
and seconds, rather than in degrees. Since the observer can 
easily find his own local time by the transit instrument, cr by 
some of the many other methods, the knot of the problem is 
simply this : To find the Greenwich time at any 'moment with- 
out going to Greenwich; then we get the longitude at once by 
merely comparing it with our own time. 

95. Methods of determining Longitude. — Incomparably the 
best method, whenever it is available, is to make a direct tele- 

1 As to the standard meridian, there is a variation of usage among dif- 
ferent nations. The French reckon from the meridian of Paris, but most 
other nations use the meridian of Greenwich, at least at sea. 



64 LOCAL AND STANDARD TIME. [§ 95 

graphic comparison between the clock of the observer and that 
of some station, the longitude of which is known. The differ- 
ence between the two clocks, duly corrected for their i errors' 
(Art. 92), will be the true difference of longitude. The astro- 
nomical difference of longitude between the two places can 
thus be determined by four or five nights' observations within 
about 0. 8 02 — i.e., within twenty feet or so, in the latitude 
of the United States. In many cases the telegraphic method, 
however, is not available ; never at sea, of course. 

96. A second method is to use a chronometer, which is 
simply a very accurate watch. This is set to Greenwich time 
at some place whose longitude is known, and afterwards is 
supposed to keep that time wherever carried. The observer 
has only to compare his own local time, determined with the 
transit instrument or sextant, with the time shown by such a 
chronometer, and the difference is his longitude from Green- 
wich. This is the ordinary method at sea. 

Practically, of course, no chronometer goes absolutely without gain- 
ing or losing; hence, it is always necessary to know and to allow for 
its gain or loss since the time it was last set. Moreover, it is never 
safe to trust a single chronometer, because of the liability of such in- 
struments to change their rate in transportation. A number should 
be used, if possible. 

Before the days of telegraphs and chronometers, astronomers 
were generally obliged to get their Greenwich time from (he 
moon, which may be regarded as a clock-hand with the stars 
for dial figures ; but observations of this kind are troublesome, 
and the results inaccurate, as compared with those obtained 
by the telegraph and chronometer. (For further details, see 
General Astronomy, Arts. 109-116.) 

97. Local and Standard Time. — Until recently it has been 
always customary to use local time, each station determining 
its own time by its own observations, and having, therefore, 






§ 97] WHERE THE DAY BEGINS. 65 

a time differing from that of all other stations not on the same 
meridian. Before the days of the telegraph, and while travel- 
ling was comparatively slow, this was best. At present there 
are many reasons why it is better to give up the old system in 
favor of a system of standard time. The change greatly facil- 
itates all railway and telegraphic business, and makes it prac- 
tically easy for everybody to have accurate time, since the 
standard time can be daily wired from some headquarters to 
every telegraph office. 

According to the system now established in North America, 
there are five such standard times in use, — the colonial, the 
eastern, the central, the mountain, and the Pacific, — which 
differ from Greenwich time by exactly four, five, six, seven, 
and eight hours respectively, the minutes and seconds being 
everywhere identical, and the same with those of the clock at 
Greenwich. In order to determine the standard time by obser- 
vation, it is only necessary to find the local time by one of the 
methods given, and correct it according to the observer's longi- 
tude from Greenwich. 

98. Where the Day begins. — It is clear that if a traveller 
were to start from Greenwich on Monday noon, and travel 
westward as fast as the earth turns to the east beneath his 
feet, he would have the sun upon the meridian all day long, 
and it would be continual noon. But what noon ? It was 
Monday when he started, and when he gets back to London 
twenty-four hours later it will be Tuesday noon there, and yet 
he has had no intervening night. When did Monday noon 
become Tuesday noon ? 

It is agreed among mariners to make the change of date at 
the 180th meridian from Greenwich. Ships crossing this line 
from the east skip one day in so doing. If it is Monday after- 
noon when a ship reaches the line, it becomes Tuesday after- 
noon the moment she passes it, the intervening twenty-four 
hours being dropped from the reckoning on the log-book. 



66 POSITION OF A HEAVENLY BODY. [§W 

Vice rcrs(U when a vessel crosses the line from the western 
Bide, it counts the same day twioe, passing from Tuesday back 
to Monday, 

This 180th meridian passes mainly over the ocean, hardly touching 
land anywhere. There is some irregularity as to the date actually 
used on fche different islands of the Paoific. Those which received 
their earliest European inhabitants via the Cape of Good Elope, hare, 

for the most part, adopted the Asiatic date, even it* they really lie cast 

of the isoth meridian, while those which were first approached via 

Cape Horn have the American date. When Alaska was transferred 
from Russia to the United States,, it was necessary to drop one day o( 

the week Erom the official dates. 



DETERMINATION OV THE POSITION OF A HEAVENLY 

BODY. 

As the basis o( our investigations in regard to the motions 

oi' the heavenly bodies, wo require a knowledge of their 

places in the sky at known times. By the "place" of a body, 

wo moan its right ascension and declination. 

99. By the Meridian Circle ^see Appendix, Art. 418), — If a 
body is bright enough to be seen by the telescope of the merid- 
ian circle, and comes to the meridian in the night-time, its 
right ascension and declination are best determined by that 
instrument. If the instrument-is in exact adjustment, the 
right ascension oi' the body is simply the sidereal time when it 
crosses the middle vertical wire o( the reticle. The 'circle- 
reading,' on the other hand, corrected for refraction, gives the 
declination. A single complete observation with the meridian 
circle determines accurately both the right ascension and the 
declination o( the object, 

100. By the Equatorial. — 1 f the body — a comet, for instance 
— is too faint to be observed by the telescope of the meridian 
circle, seldom very powerful, or comes to the meridian only in 



§ 100J DETERMINATION OF POSITION. 67 

the daytime, we usually accomplish our object by using the 
equatorial (Appendix, Art. 414), and determine the position 
of the body by measuring with some kind of ( micrometer' 
the difference of right ascension and declination between it 
and a neighboring star whose place is given in some star^ 
catalogue. 



68 THE EARTH. [§ 101 



CHAPTER IV. 

THE EARTH : ITS FORM AND DIMENSIONS ; ITS ROTATION, 
MASS, AND DENSITY; ITS ORBITAL MOTION AND THE 
SEASONS. — PRECESSION. — THE YEAR AND THE CAL- 
ENDAR. 

101. In a science which deals with the ' heavenly bodies/ 
there might seem at first no place for the Earth. But certain 
facts relating to the Earth, just such as we have to investi- 
gate with respect to her sister planets, are ascertained by astro- 
nomical methods, and a knowledge of them is essential as a 
base of operations. In fact, Astronomy, like charity, "begins 
at home/' and it is impossible to go far in the study of the 
bodies which are strictly "heavenly" until we have first ac- 
quired some accurate knowledge of the dimensions and motions 
of the Earth itself. 

102. The astronomical facts relating to the Earth are 
broadly these : — 

1. The earth is a great ball about 7920 miles in diameter. 

2. It rotates on its axis once in twenty-four " sidereal " 
hours. 

3. It is not exactly spherical, but is slightly flattened at the 
poles ; the polar diameter being nearly twenty-seven miles, or 
about b 1q part less than the equatorial. 

4. It has a mean density of about 5.6 times that of water, 
and a mass represented in tons by 6 with twenty-one ciphers 
following, (six thousand millions of millions of millions of 
tons.) 

5. It is flying through space in its orbital motion around 
the sun, with a velocity of about eighteen and a half miles a 



§ 102] THE EAUTH'S FORM AND SIZE. 69 

second ; i. e., about seventy-five times as swiftly as an ordinary 
cannon-ball, 

103. The Earth's Approximate Form and Size. — It is not 

necessary to dwell on the ordinary proofs of the earth's globu- 
larity. We simply mention them. 

1. It can be sailed around. 

2. The appearance of vessels coming in from the sea indi- 
cates that the surface is everywhere convex. 

3. The fact that as one goes from the equator towards the 
north the elevation of the pole increases in proportion to the 
distance from the equator, proves the same thing. 

4. The outline of the earth' s shadow, as seen upon the moon 
during lunar eclipses, is such as only a sphere could cast. 

We may add, as to the smoothness and roundness of the 
earth, that if the earth be represented by an eighteen-inch 
globe, the difference between its greatest and least diameters 
would be only about one-sixteenth of an inch ; the highest 
mountains would project only about one-seventieth of an inch, 
and the average elevation of continents and depths of the 
ocean would be hardly greater than a film of varnish. Rela- 
tively, the earth is really much smoother and rounder than 
most of the balls in a bowling-alley. 

104. One of the simplest methods of showing the curvature of the 
earth is the following : — 

In an expanse of still, shallow water (a long reach of canal, for 
instance), set a row of three poles about a mile apart, with their tops 
projecting to exactly the same height above the surface. On sighting 
icross, it will then be found that the middle pole projects about eight 
inches (when refraction has been allowed for) above the line that 
joins the tops of the two end ones, and from this a rough estimate of 
the size of the earth can be made (see General Astronomy, Art. 134). 

105. Measure of the Earth's Diameter. — The only accurate 
method of measuring the diameter of the earth is the follow- 



70 



THE EARTHS DIAMETER. 



[§105 



ing, the principle of which is very simple, and should be thor- 
oughly mastered by the student : — 

It consists in rinding the length in miles of an arc of the 
earth's surface containing a known number of degrees. From 

this we get the length of one degree, 
and this gives the circumference of 
the earth (since it contains 360°), 
and from this the diameter is ob- 
tained by dividing it by 3.14159. 

To do this, we select two sta- 
tions, a and b (Fig. 8), some hun- 
dreds of miles apart on the same 
meridian, and determine the lati- 
tude (or the altitude of the pole) at 
each station by astronomical obser- 
vation. The difference of latitude 
(i.e., ECb — ECa) is evidently the 
number of degrees in the arc ab, 
and the determination of this dif- 
ference of latitude is the only astro- 
nomical operation necessary. 

Next, the distance in miles be- 
tween the two stations must be 
measured. This is geodetic work, and it is enough for our 
purpose here to say that it can be done with great precision by 
a process which is called i triangulation.' 

This measuring of arcs has been done on many parts of the 
earth's surface, and the result is that the average length of a 
degree is found to be a little more than sixty-nine miles, and 
the mean diameter of the earth about 7918 miles. The reason 
why we say average length and mean diameter is that the 
earth, as has been said, is not quite a globe, but is slightly 
flattened at its poles, so that the lengths of the degrees dif- 
fer in different parts of the earth, as we shall soon see (Art. 
110). 




Fig. 8. - 



■ Measuring the Earth's 
Diameter. 



§ 106] THE ROTATION OF THE EARTH. 71 

106. The Rotation of the Earth. — Ptolemy understood that 
the earth was round, but he and all his successors deliberately 
rejected the theory of its rotation. Though the idea that the 
earth might turn upon an axis was not unfamiliar, they con- 
sidered that there were conclusive reasons against it. At the 
time when Copernicus of Thorn, in Poland (1473-1543), pro- 
posed his theory of the solar system, the only argument he 
could urge in favor of the earth's rotation 1 was that this 
hypothesis was much more probable than the older one that 
the heavens themselves revolve. All the phenomena then 
known would be sensibly the same on either supposition. The 
apparent daily motion of the heavenly bodies can be perfectly 
accounted for (within the limits of such observations as were 
then possible) either by supposing that they are actually at- 
tached to the celestial sphere, which turns daily, or that the 
earth itself spins upon an axis once in twenty-four hours ; and 
for a long time the latter hypothesis did not seem to most 
people so reasonable as the older and more obvious one. A 
little later, after the telescope had been invented, analogy 
could be appealed to ; for we can see with the telescope that 
the sun and moon and many of tKe planets really rotate upon 
axes. At present we can go still farther, and can absolutely 
demonstrate the earth's rotation by experiments, some of 
which even make it visible. 

107. Foucault's Pendulum Experiment. — Among these ex- 
perimental proofs, the most impressive is the " pendulum 
experiment" devised by Foucault in 1851. From the dome 
of the Pantheon, in Paris, he hung a heavy iron ball by a 
slender wire more than 200 feet long (Fig. 9). A circular rail, 

1 The word rotation denotes a spinning motion, like that of a wheel on 
its axis. The word revolve is more general, and may be used to describe 
such a spinning motion, or (and this is the more common use in Astron- 
omy) to describe the motion of a body travelling around another, as when 
we say the earth * revolves ' around the sun. 



72 



foucault's pendulum experiment. 



[§107 




with a little ridge of sand built upon it, was placed in such a 
way that a pin attached to the swinging ball would just scrape 

the sand and leave a mark at 
each vibration. To put the 
ball in motion, it was drawn 
aside by a cotton cord and 
left for some hours, until 
it came absolutely to rest. 
Then the cord was burned 
off, and the pendulum started 
to swing in a true plane. 

But this plane at once be- 
gan to deviate slowly towards 
the right, so that the pin on 
the pendulum ball cut the 
sand ridge in a new place at 
each swing, shifting at a rate 
which would carry the line 
fully around in about thirty- 
two hours, if the pendulum 
did not first come to rest. In 
fact, the floor was actually 




Fig. 9. — Foucault's Pendulum Experiment. 



and visibly turning under the plane defined by the swinging 
of the pendulum. 

The experiment created great enthusiasm at the time, and has since 
been frequently performed. The pendulum used in such experiments 
must, in order to secure success, have a round ball, must be suspended 
by a round wire or on a point, and must be very heavy, very long, and 
very carefully protected against currents of wind. At the pole the 
plane of the pendulum will shift completely around once in twenty- 
four hours ; at the equator, it will not turn at all ; and in the interme- 
diate regions, it will shift more or less rapidly according to the latitude 
of the place where the experiment is performed. (For fuller descrip- 
tion, see General Astronomy, Arts. 140, 141.) 

There are a number of other experimental proofs of the earth's rota- 
tion, which are really just as conclusive as the one above cited. (Gen- 
eral Astronomy, Arts. 138-144.) 



§ 108 ] THE EARTH'S ROTATION". 73 

108. Invariability of the Earth's Rotation. — It is a question 
of great importance whether the day ever changes its length. 
Theoretically, it must almost necessarily do so. The friction 
of the tides and the fall of meteors upon the earth both tend 
to retard the rotation, while, on the other hand, the earth's 
loss of heat by radiation and the consequent shrinkage of the 
globe must tend to accelerate it, and to shorten the day. Then 
geological changes, the elevation and subsidence of continents, 
and the transportation of soil by rivers, act, some one way and 
some the other. At present we can only say that the change, 
if any change has occurred since Astronomy became accurate, 
has been too small to be detected. The day is certainly not 
longer or shorter by the y^ part of a second than it was in 
the days of Ptolemy; probably it has not changed by the 
y^q^ part of a second, though of that we can hardly be sure. 

109. Shiftings of the Earth's Axis. — Theoretically, any changes 
in the distribution of materials within or upon the globe of the earth 
ought to produce corresponding displacements of the axis, and these 
would principally show themselves as variations in the latitudes and 
longitudes of observatories. The actual variations are so minute, how- 
ever, that it is only as recently as 1889 that they were first clearly 
detected by certain German observers, whose results have since been 
abundantly confirmed and extended. It is now beyond doubt that 
the earth really " wobbles " in whirling ; and this causes each pole to 
describe an apparently irregular path around its mean position, never 
departing from it, however, by more than 40 or 50 feet. Dr. Chandler 
has shown that this motion is compounded of two, one circular, with 
a period of a year, the other oval, with a period of 428 days. 

To explain certain geological phenomena it has been surmised 
that great and permanent displacements of the poles have occurred 
in the distant past. But of this, we have, as yet, no satisfactory 
evidence. 

110. Effect of the Earth's Rotation on its Form. — The 

whirling of the earth on its axis tends to make the globe 
bulge at the equator and flatten at the poles, in the way illus- 



74 



THE EARTH'S ROTATION. 



[§110 



trated by the well-known little apparatus shown in Fig. 10. 

That the equator does really bulge in this way is shown by 

measuring the length of a 
degree of latitude on the va- 
rious parts of the eartKs 
surface between the equator 
and the pole, in the manner 
indicated a few pages back 
(Art. 105). More than 
twenty such arcs have been 
measured, and it appears 
that the length of the de- 

PIG. 10. — Effect of Earth's Rotation on its Form. g-pgQg increases regularly 

from the equator towards the poles, as shown in the following 
table : — 

At the equator, one degree = 68.704 miles 




At lat. 20° 


a 


a 


= 68.786 " 


« « 4.Q0 


a 


a 


= 68.993 " 


" " 60° 


a 


a 


= 69.230 " 


" « 80° 


a 


u 


= 69.386 " 


At the pole, 


u 


a 


= 69.407 « 



The difference between the equatorial and polar degree of 
latitude is more than 0.7 of a mile, or over 3700 feet, while 
the probable error of measurement cannot exceed a foot or 
two to the degree. 

Prom this table it can be calculated, by methods which 
cannot be explained without assuming too much mathematical 
knowledge in our readers, that the earth is orange-shaped, or 
"an oblate spheroid," the diameter from pole to pole being 
7899.74 miles, while the equatorial diameter is 7926.61 miles. 
The difference, 26.87 miles, is about -^-^ of the equatorial 
diameter. This fraction, -j^, is called the oblateness or ellip- 
ticity of the earth. 

Scholars are often puzzled by the fact that although the pole is 
nearer the centre of the earth than the equator, yet the degrees of lat- 



§ HO] SURFACE AND VOLUME OF THE EARTH. 



75 




itude are longest at the pole. It is because the earth's surface there is 
more nearly flat than anywhere else, so that a person has to travel 
more miles to change the 
direction of his plumb- a \ ^P \b 

line one degree. Fig. 11 
illustrates this. The an- 
gles adb and fhg are equal, 
but the arc ab is longer 
than fg. 

111. Effect of 
Earth's Rotation 

Ellipticity UPOII the Fig.II. — Length of Degrees in Different Latitudes. 

Force of Gravity. — For two reasons the force of gravity is 
less at the equator than at the poles. (1) The surface of the 
earth is there 13J miles farther from the centre, and this fact 
diminishes the gravity at the equator by about T \ z . (2) The 
centrifugal force of the earth's rotation reduces the gravity at 
the equator by about -g-g-g- ? ^ ne wn °l e reduction, therefore (-^g- 
-f- 2^-9), is very nearly equal to y^ ; i.e., an object which weighs 
190 pounds at the equator would weigh 191 pounds near the pole, 
— weighed by an accurate spring-balance. (In an ordinary bal- 
ance, the loss of weight would not show, simply because the 
weights themselves would be affected as much as the body 
weighed, so that the balance would not be disturbed.) The 
effect of this variation of gravity from the pole to the equator 
is especially evident in the going of a pendulum clock. Such 
a clock, adjusted to keep accurate time at the equator, would 
gain 3 m 37 s a day near the pole. In fact, one of the best ways 
of determining the form of the earth is by experiments with a 
pendulum at stations which differ considerably in latitude. 



112. Surface and Volume of the Earth. — The earth is so 
nearly spherical that we can compute its surface and volume 
with sufficient accuracy by the formula for a perfect sphere, 
provided we put the earth's mean semi-diameter for the radius 



76 the earth's mass and density. [§ 112 

of the sphere. This mean semi-diameter is not the average of 
the polar and equatorial diameters, but is found by adding the 
polar diameter to twice the equatorial, and dividing by three. 
It comes out 7917.66 miles. From this we find the earth's 
surface to be, in round numbers, 197,000000 square miles, and 
its volume, or bulk, 260000,000000 cubic miles. 

113. The Earth's Mass and Density. — The volume (or bulk) 
of a globe is simply the number of cubic miles of space which 
it contains. If the earth were all made of feathers or of lead, 
its volume would remain the same, as long as the diameter 
was not altered. The earth's mass, on the other hand, is the 
quantity of matter in it — the number of tons of rock and 
water which compose it, — and of course it makes a great dif- 
ference with this whether the material be heavy or light. 
The density of the earth is the number of times its mass 
exceeds that of a sphere of pure water having the same 
dimensions. 

The methods by which the mass of the earth can be measured 
depend upon a comparison between the attraction which the earth 
exerts upon a body at its surface and the attraction which is exerted 
upon the same body by another large body of known mass and at a 
known distance. The experiments are delicate and difficult, and we 
must refer for details to our larger book, General Astronomy, Arts. 
164-179. 

According to the best data at present available the earth's 
density is about 8.58, and its mass about 6000 millions of 
millions of millions of tons. 

The most recent and valuable determinations are those 
made at Potsdam in 1888, and by Boys in England in 1893. 
Another is now in progress at Berlin. 

114. Constitution of the Earth's Interior. — Since the average 
density of the earth's crust does not exceed three times that 
of water, while the mean density of the whole earth is about 
5.58, it is clear that at the earth's centre the density must be 



§ 114] THE SUN AND THE EARTH. 77 

very much greater than at the surface. Very likely it is as 
high as eight or ten times the density of water, and equal to 
that of the heavier metals. 

There is nothing surprising in this. If the earth were once fluid, it 
is natural to suppose that the densest materials, in the process of 
solidification, would settle towards the centre. 

Whether the centre of the earth is now solid or fluid, it is difficult 
to say with certainty. Certain tidal phenomena, to be mentioned 
hereafter, have led Lord Kelvin to conclude that the earth as a whole 
is probably solid throughout and "more rigid than glass," volcanic cen- 
tres being mere "pustules," so to speak, in the general mass. To this 
most geologists demur, maintaining that at the depth of not many 
hundred miles the materials of the earth must be fluid, or at least 
semi-fluid. They infer this from the phenomena of volcanoes, and 
from the fact that the temperature continually increases with the 
depth, so far at least as we have yet been able to penetrate. 

THE APPARENT MOTION OF THE SUN AND THE ORBITAL 
MOTION OF THE EARTH, AND THEIR IMMEDIATE CON- 
SEQUENCES. 

115. The Sun's Apparent Motion among the Stars. — The 

sun's apparent motion among the stars, which makes it describe 
the circuit of the heavens once a year, must have been among 
the earliest recognized astronomical phenomena, as it is one 
of the most important. The sun, starting in the spring, 
mounts northward in the sky each day at noon for three 
months, appears to stand still a few days at the summer sol- 
stice, and then descends towards the south, reaching in autumn 
the same noon-day elevation which it had in the spring. It 
keeps on its southward course to the winter solstice (in Decem- 
ber), and then returns to its original height at the end of a 
year, by its course causing and marking the seasons. 

Nor is this all. The sun's motion is not merely north and 
south, but it also advances continually eastward among the stars. 
It is true that we cannot see the stars near the sun in the 



78 THE ECLIPTIC. [§ n ^ 

same way that we can those about the moon, so as to be able 
directly to perceive this motion ; but in the spring the stars 
which are rising in the eastern horizon are different from 
those which are found there in the summer or in the winter. 
In March the most conspicuous of the eastern constellations 
at sunset are Leo and Bootes. A little later Virgo appears ; in 
the summer Ophiuchus and Libra ; still later Scorpio ; while 
in midwinter Orion and Taurus are ascending as the sun goes 
down. 

So far as the obvious appearances are concerned, it is quite 
indifferent whether we suppose the earth to revolve around 
the sun, or vice versa. That the earth really moves, however, 
is absolutely demonstrated by two phenomena too minute and 
delicate for observation without the telescope, but accessible 
to modern methods. One of them is the aberration of light, 
the other the annual parallax of the fixed stars. These can be 
explained only by the actual motion of the earth, but we post- 
pone their discussion for the present (see Art. 343, and Appen- 
dix, 435). 

116. The Ecliptic; its Related Points and Circles. — By ob- 
serving daily with the meridian circle the sun's declination 
and the difference between its right ascension and that of 
some standard star, we obtain a series of positions of the sun's 
centre which can be plotted on the globe, and we can thus 
mark out the path of the sun among the stars. It turns out 
to be a great circle, as is shown by its cutting the celestial equa- 
tor at two points just 180° apart (the so-called " equinoctial 
points" or "equinoxes"), where it makes an angle with the 
equator of approximately 23|° (23° 27' 14" in 1890). 

This great circle is called the Ecliptic, because, as was early 
discovered, eclipses happen only when the moon is crossing 
it. Its position among the constellations is shown upon the 
equatorial star-maps. It may be defined as the circle in which 
the plane of the earth's orbit cuts the celestial sphere. 



§ 116] THE ZODIAC. 79 






The angle which the ecliptic makes with the equator at the 
equinoctial points is called the obliquity of the Ecliptic. This 
obliquity is evidently equal to the sun's greatest distance from 
the equator ; i.e., its maximum declination, which is reached in 
December and June. 



117. The two points in the ecliptic midway between the 
equinoxes are called the solstices, because at these points the 
sun " stands " ; that is, ceases to move north or south. Two 
circles drawn through the solstices parallel to the equator are 
called the tropics, or " turning-lines," because there the sun 
turns from its northward motion to the southward, or vice 
versa. The two points in the heavens 90° distant from the 
ecliptic are called the poles of the ecliptic. The northern one 
is in the constellation of Draco, about midway between the 
stars Delta and Zeta Draconis, at a distance from the pole of 
the heavens equal to the obliquity of the ecliptic, or about 
23 \°, and on the Solstitial Colure, the hour-circle which runs 
through the two solstices; the hour-circle which passes through 
the equinoxes being called the Equinoctial Colure. Great 
circles drawn through the poles of the ecliptic, and therefore 
perpendicular, or " secondaries," to the ecliptic, are known as 
circles of latitude. It will be remembered (Art. 20) that celes- 
tial longitude and latitude are measured with reference to the 
ecliptic, and not to the equator. 

118. The Zodiac and its Signs. — A belt 16° wide (8° on 
each side of the ecliptic) is called the Zodiac, or zone of ani- 
mals, the constellations in it, excepting Libra, being all figures 
of animals. It is taken of that particular width simply 
because the moon and all the principal planets always keep 
within it. It is divided into the so-called signs, each 30° in 
length, having the following names and symbols : — 



80 the earth's ORBIT. [§ 118 

( Aries °f ( Libra =2= 

Spring < Taurus 8 Autumn I Scorpio ^ 

( Gemini n ( Sagittarius / 

( Cancer 03 ( Capricornus VJ 

Summer I Leo SI Winter < Aquarius zz 

( Virgo tr# ( Pisces X 

The symbols are for the most part conventionalized pictures of the 
objects. The symbol for Aquarius is the Egyptian character for 
water. The origin of the signs for Leo, Capricornus, and Virgo is 
not quite clear. 

The zodiac is of extreme antiquity. In the zodiacs of the 
earliest history, the Fishes, Earn, Bull, Lion, and Scorpion 
appear precisely as now. 

119. The Earth's Orbit. — The ecliptic must not be con- 
founded with the earth's orbit. It is simply a great circle of 
the infinite celestial sphere, — the trace made upon that sphere 
by the plane of the earth's orbit, as was stated in its definition. 
The fact that the ecliptic is a great circle gives us no informa- 
tion about the earth's orbit itself, except that it lies in one 
plane passing through the sun. It tells us nothing as to the 
orbit's real form and size. 

By reducing the observations of the sun's right ascension 
and declination through the year to longitude and latitude 
(the latitude would always be exactly zero except for some 
slight perturbations due chiefly to the moon's revolution 
around the earth), and combining these data with observations 
of the sun's apparent diameter, we can, however, ascertain the 
form of the earth's orbit and the law of its motion. The size 
of the earth's orbit, i.e., its scale of miles, cannot be fixed until 
we find the sun's distance. 

The result is that the orbit is found to be very nearly a 
circle, but not exactly so. It is an oval or ellipse, with the sun 
at one of its foci (as illustrated in Fig. 12), but is much more 



119] 



DEFINITION OF TERMS. 



81 



nearly circular than the oval there represented. Its eccen- 
tricity is only about -^ ; that is to say, the distance from the 
centre of the sun to the mid- 
dle of the ellipse is only about 
-gL- of the average distance of 
the sun from the earth. 

The method by which we 
proceed to ascertain the form 
of the orbit may be found in 
the Appendix, Art. 428. For 
a description of the ellipse, 
see Art. 429. 




Fig. 12. — The Ellipse. 



120. Definition of Terms. — The points where the earth is 
nearest to and most remote from the sun are called respec- 
tively the Perihelion and the Aphelion (Dec. 31st and June 
30th), the line joining them being the Major-axis of the orbit. 
This line, indefinitely produced in both directions, is called 
the 'Line of Apsides' (pronounced Ap'-si-deez), the major axis 
being a limited piece of it. A line drawn from the sun to the 
earth, or to any other planet at any point in its orbit, as SP in 
Fig. 12, is called the planet's Radius Vector. 

The variations in the sun's apparent diameter due to our 
changing distance are too small to be detected without a 
telescope, so that the ancients failed to perceive them. Hip- 
parchus, however, about 120 B.C., discovered that the earth is 
not in the centre * of the circular orbit which he supposed the 
sun to describe around it with uniform velocity. 

Obviously the sun's apparent motion is not uniform, because 
it takes 186 days for the sun to pass from the vernal equinox, 

1 Hipparchus (and every one else until the time of Kepler, 1607) 
assumed on metaphysical grounds that the sun's orbit must necessarily 
be a circle, and described with a uniform motion, because (they said) the 
circle is the only perfect curve, and uniform motion is the only perfect 
motion proper for heavenly bodies. 




82 LAW OF THE EARTH'S MOTION. [§ 120 

March 20th, to the autumnal, Sept. 22d and only 179 days to 
return. Hipparchus explained this on the hypothesis that the 
earth is out of the centre of the circle. 

121. The Law of the Earth's Motion. — By combining the 
measured apparent diameter of the sun with the differences of 
longitude from day to day, we can deduce mathematically not 

only the form of the earth's or- 
bit, but the law of her motion in 
it. It can be shown from the 
comparison that the earth moves 
in such a way that its radius 
vector describes areas proportional 
to the time, a law which Kepler 
first brought to light in 1609; 
that is to say, if ah, cd, ef (Fig. 

Fig. 13. — Equable Description of Areas. -. \ i j. • £ ±.\ i • ±. i 

13) be portions ol the orbit de- 
scribed by the earth in different weeks, the areas of the ellip- 
tical sectors aSb, cSd, and eSf are all equal. A planet near 
perihelion moves faster than at aphelion in just such propor- 
tion as to preserve this relation. 

As Kepler left the matter, this is a mere fact of observation. 
Newton afterwards proved that it is the necessary mechanical 
consequence of the fact that the earth moves under the action 
of a force always directed towards the sun. 

It is true in every case of the elliptical motion of a heavenly body, 
and enables us to find the position of the earth or of any planet, when 
we once know the time of its orbital revolution (technically the 
"period "), and the time when it was last at perihelion. The solution 
of the problem, first worked out by Kepler, lies, however, quite beyond 
the scope of the present work. 

122. Changes in the Earth's Orbit. — The orbit of the earth 
changes slowly in form and position, though in the long run 
it is absolutely unchangeable as regards the length of its 
major axis and the duration of the year. 



1 122] 



THE SEASONS. 



83 



These so-called "secular changes" are due to "perturba- 
tions" caused by the action of the other planets upon the 
earth. Were it not for their attraction the earth would keep 
her orbit with reference to the sun and stars absolutely 
unaltered from age to age. 

Besides these secular perturbations of the earth's orbit, the 
earth itself is also continually being slightly disturbed in its 
orbit. On account of its connection with the moon, it oscil- 
lates each month a few hundred miles above and below the 
true plane of the ecliptic, and by the action of the other 
planets is sometimes set backwards or forwards in its orbit to 
the extent of some thousands of miles. Of course every such 
displacement of the earth produces a corresponding slight 
change in the apparent position of the sun and of the nearer 
planets. 



Autumnal Equinox 




Vernal Equinox 
Fig. 14. — The Seasons 



123. The Seasons. — The earth in its motion around the sun 
always keeps its axis nearly parallel to itself during the whole 
year, for the mechanical reason that a spinning globe main- 




84 THE SEASONS. [§ 12 ^ 

tains the direction of its axis invariable, unless disturbed by 
some outside force (very prettily illustrated by the gyro- 
scope). Fig. 14 shows the way in which the north pole of 
the earth is tipped with reference to the sun at different 
seasons of the year. At the vernal equinox (March 20th) the 
earth is situated so that the plane of its equator passes 
through the sun. At that time, therefore, the circle which 
bounds the illuminated portion of the earth passes through 
the two poles, as shown in Fig. 15, _B, and day and night are 

therefore equal, as implied by the 
term ' equinox.' The same is again 
true on the 22d of September. 
I About the 21st of June the earth is 
so situated that its north pole is 
inclined towards the sun by about 

Fig. 15. -Position of Pole at Solstice 23 J°, as shown in Fig. 15, A. The 

and Equinox. south pole is then in the unlighted 

half of the earth's globe, while the north pole receives sunlight 
all day long, and in all portions of the northern hemisphere 
the day is longer than the night. In the southern hemi- 
sphere, on the other hand, the reverse is true. 

At the time of the winter solstice the southern pole has per- 
petual sunshine, and the north pole is in the night. At the 
equator of the earth, day and night are equal at all times of 
the year, and at that part of the earth there are no seasons in 
the proper sense of the word. Everywhere else the day and 
night are unequal, except when the sun is at one of the 
equinoxes. 

In high latitudes the inequality between the lengths of the 
day in summer and in winter is very great ; and at places 
within the polar circle there are always days in winter when 
the sun does not rise at all, and others in the summer when it 
does not set, but we have the phenomenon of the "midnight 
sun," as it is called. At the pole itself, the summer is one 
perpetual day, six months in length, while the winter is a six- 
months night. 



§123] 



EFFECTS ON TEMPERATURE. 



85 



Perhaps the student will get a better idea by thinking of the earth 
as a globe floating, just half immersed, on a sheet of still water, and so 
weighted that its poles dip at an angle of 23J°, while it swims in a 
circle around the sun, a much larger globe, also floating on the same 
surface. The sheet of water corresponds to the ecliptic, while the 
plane of the equator is a circle on the globe itself, drawn square to the 
axis. If, now, the axis is kept pointing always the same way while 
the globe swims around, things will correspond to the motion of the 
earth around the sun. 




124. Effects on Temperature. — The changes in the dura- 
tion of insolation (exposure to sunshine) at any place involve 
changes of temperature, thus producing the seasons. It is 
clear that the surface of the soil at any place in the northern 
hemisphere will receive daily from the sun more than the 
average amount of heat when- 
ever he is north of the celestial 
equator, and for two reasons : — 

1. Sunshine lasts more than 
half the day. 

2. The mean altitude of the 
sun during the day is greater 
than the average for the year, 
since he is higher at noon than 
at the time of the equinox, and 
in any case reaches the horizon at rising and setting. 

Now the more obliquely the rays strike, the less heat they 
bring to each square inch of surface, as is obvious from Fig. 
16. A beam of sunshine which would cover the surface AC, 
if received squarely, will be spread over a much larger sur- 
face, Ac, if it falls at the angle h. The difference in favor of 
vertical rays is further exaggerated by the absorption of heat 
in our atmosphere, because the rays that are nearly horizontal 
have to traverse a much greater thickness of air before reach- 
ing the ground. 

For these two reasons, therefore, the temperature rises 



Fig. 16. 

Effect of Sun's Elevation on Amount of 

Heat imparted to the Soil. 



86 PRECESSION OF THE EQUINOXES. [§ 124 

rapidly for a place in the northern hemisphere as the sun 
comes north of the equator. We, of course, receive the most 
heat in twenty -four hours at the time of the summer solstice; 
but this is not the hottest time of the summer. The weather 
is then getting hotter, and the maximum will not be reached 
until the increase ceases; i.e., not until. the amount of heat 
lost in twenty-four hours equals that received in the same 
time. This maximum is reached in our latitude about the 1st 
of August. For similar reasons the minimum temperature in 
winter occurs about Feb. 1st. 

125. Precession of the Equinoxes. — This is a slow westward 
motion of the equinoxes along the ecliptic. In explaining the 
seasons we have said (Art. 123) that the earth keeps its axis 
nearly parallel to itself during its annual revolution. It does 
not maintain strict parallelism, however, but owing to the 
attraction of the sun and moon on that portion of the mass of 
the earth which projects, like an equatorial ring, beyond the 
true spherical surface, the earth's axis continually but slowly 
shifts its place, keeping always nearly the same inclination to 
the plane of the ecliptic, so that its pole revolves in a small 
circle of 23^-° radius around the pole of the ecliptic once in 
25,800 years. Of course the celestial equator must move also, 
since it has to keep everywhere just 90° from the celestial 
pole ; and, as a consequence, the equinoxes move ivestward on 
the ecliptic about 50".2 each year, as if to meet the sun. 
This motion of the equinox was called i precession ? by Hip- 
parchus, who discovered 1 it about 125 B.C., but could not 
explain it. The explanation was not reached until the time of 
Newton, about 200 years ago. 

126. Effect of Precession upon the Pole and the Zodiac. — 

At present the Pole-star, Alpha Ursse Minoris, is about 1\° 

1 He discovered it by finding that in his time the place of the equinox 
among the stars was no longer the same that it used to be in the days of 
Homer and Hesiod, several hundred years before. 



§ 126] THE YEAR AND THE CALENDAR. 87 

from the pole, while in the time of Hipparchus the distance 
was fully 12°. During the next century the distance will 
diminish to about 30', and then begin to increase. 

If upon the celestial globe we trace a circle of 23^-° radius, 
around the pole of the ecliptic as a centre, it will mark the 
track of the celestial pole among the stars. 

It passes not very far from Alpha Lyrse (Vega), on the opposite 
side of the circle from the present Pole-star ; about 12,000 years hence 
Vega will, therefore, be the Pole-star. Reckoning backwards, we find 
that some 4000 years ago Alpha Draconis (Thuban) was the Pole-star, 
and about 3J° from the pole. 

Another effect of precession is that the signs of the zodiac 
do not now agree with the constellations which bear the same 
name. The sign of Ares is now in the constellation of Pisces, 
and so on ; each sign having " backed " bodily, so to speak, 
into the constellation west of it. 

The forces which cause precession do not act quite uni- 
formly, and as a result the rapidity of the precession varies 
somewhat, and there is also a slight tipping or nodding of the 
earth's axis which is called nutation. (For a fuller account of 
the whole matter, see General Astronomy, Arts. 209-215.) 



THE YEAR AND THE CALENDAR 

127. Three different kinds of "year" are now recognized, 
— the Sidereal, the Tropical (or Equinoctial), and the Anom- 
alistic. 

The sidereal year, as its name implies, is the time occu= 
pied by the sun in apparently completing the circuit from a 
given star to the same star again. Its length is 365 days, 
6 hours, 9 minutes, 9 seconds. From the mechanical point of 
view, this is the true year; i.e., it is the time occupied by the 
earth in completing its revolution around the sun from a given 
direction in space to the same direction again. 



88 THE CALENDAR. [§ 127 

The tropical year is the time included between two successive 
passages of the vernal equinox by the sun. Since the equinox 
moves yearly 50".2 towards the west, the tropical year is 
shorter than the sidereal by about 20 minutes, its length being 
365 days, 5 hours, 48 minutes, 46 seconds. Since the seasons 
depend on the sun's place with respect to the equinox, the tropical 
year is the year of chronology and civil reckoning. 

The third kind of year is the anomalistic year, — the time between 
two successive passages of the perihelion by the earth. Since the line 
of apsides of the earth's orbit makes an eastward revolution once in 
about 108,000 years, this kind of year is nearly 5 minutes longer than 
the sidereal, its length being 365 days, 6 hours, 13 minutes, 48 sec- 
onds. It is but little used except in calculations relating to perturba- 
tions of the planets. 

128. The Calendar. — The natural units of time are the 
day, the month and the year. The day is too short for con- 
venience in dealing with considerable periods, such as the life 
of a man, for instance ; and the same is true even of the 
month ; so that for all chronological purposes the tropical year 
(the year of the seasons) has always been employed. At the 
same time, so many religious ideas and observations have been 
connected with the changes of the moon, that there has been a 
constant struggle to reconcile the month with the year. Since 
the two are incommensurable, no really satisfactory solution is 
possible, and the modern calendar of civilized nations entirely 
disregards the lunar phases. In early times the calendar was 
in the hands of the priesthood, and was mainly lunar, the 
seasons being either disregarded, or kept roughly in place 
by the occasional putting in or dropping of a month. The 
Mohammedans still use a purely lunar calendar, having a 
"year" of twelve months, which contains alternately 354 and 
355 days. In their reckoning the seasons fall continually in 
different months, and their calendar gains on ours about one 
year in thirty-three. 



§ 129] THE JULIAN CALENDAR. 89 






129. The Julian Calendar. — When Julius Caesar came into 
power, he found the Eonian calendar in a state of hopeless 
confusion. He, therefore, with the advice of Sosigenes, the 
astronomer, established (b.c. 45) what is known as the Julian 
Calendar, which still, either untouched or with a trifling mod- 
ification, continues in use among civilized nations. Sosigenes 
discarded all reference to the moon's phases, and adopting 
365^ days as the true length of the year, he ordained that 
every fourth year should contain 366 days, — the extra day 
being inserted by repeating the sixth day before the Calends 
of March (whence such a year is called " Bissextile "). He 
also transferred the beginning of the year, which before 
Caesar's time had been in March (as is indicated by the names 
of several of the months, — December, the tenth month, for 
instance), to Jan. 1st. 

Caesar also took possession of the month Quintilis, naming it July 
after himself. His successor, Augustus, in a similar manner appropri- 
ated the next month, Sextilis, calling it August, and to vindicate his 
dignity and make his month as long as his predecessor's he added tc 
it a day stolen from February. 

The Julian calendar is still used unmodified in the Greek 
Church, and also in many astronomical reckonings. 

130. The Gregorian Calendar. — The true length of the 
tropical year is not 365^ days, but 365 days, 5 hours, 48 min- 
utes, 46 seconds, leaving a difference of 11 minutes and 14 
seconds by which the Julian year is too long. This difference 
amounts to a little more than three days in 400 years. As a 
consequence the date of the vernal equinox comes continually 
earlier and earlier in the Julian calendar, and in 1582 it had 
fallen back to the 11th of March instead of occurring on the 
21st, as it did at the time of the Council of Nice (a.d. 325). 
Pope Gregory, therefore, under the astronomical advice of 
Clavius, ordered that the calendar should be restored by add- 
ing ten days, so that the day following Oct. 4th, 1582, should 



THE GKEG0K1AJS CALENDAR. [§ 130 

called the loth instead of the oth : further, to prevent any 
future displacement of the equinox, he decreed that thereafter 
only such centuiy years should be leap years as are divisible 
by 400. Thus 1700. 1800, 1900. and 2100 are not leap 

vs. but 1600 and - :;. The change was immediately 

pted by all ( ek Church and 

most Protes - ; fused to iv g - au- 

thor::)-. Hie new calendar was, however. 1 in 

gland in 1752. A: present (since the year 18 sal 

year in the Julian cale: I not in the Gregorian^* the dif- 

Lendars is i lays 5 but it will 

become thirteen in 1900, which will not be a leap year with 
us, though it will in Rossi; 



§ 131] THE MOON. 91 



CHAPTER V. 

THE MOON. — HER ORBITAL MOTION AND THE MONTH. — 
DISTANCE, DIMENSIONS, MASS, DENSITY, AND FORCE OF 
GRAVITY. — ROTATION AND L1BRATIONS. — PHASES. — 
LIGHT AND HEAT. — PHYSICAL CONDITION. — TELE- 
SCOPIC ASPECT AND PECULIARITIES OF THE LUNAR 
SURFACE. 

131. Xext to the sun, the moon is the most conspicuous, 
and to us the most important, of the heavenly bodies ; in fact, 
she is the only one except the sun, which exerts the slightest 
perceptible influence upon the interests of human life. She 
owes her conspicuousness and her importance, however, solely 
to her nearness ; for she is really a very insignificant body as 
compared with stars and planets. 

132. The Moon's Apparent Motion; Definition of Terms, etc. 

— One of the earliest observed of astronomical phenomena 
must have been the eastward motion of the moon with refer- 
ence to the sun and stars, and the accompanying change of 
phase. If, for instance, we note the moon to-night as very 
near some conspicuous star, we shall find her to-morrow night 
at a point considerably farther east, and the next night 
farther yet ; she changes her place about 13° daily, and makes 
the complete circuit of the heavens, from star to star again, in 
about 27^ days. In other words, she revolves around the 
earth in that time, while she accompanies us in our annual 
journey around the sun. Since the moon moves eastward 
among the stars so much faster than the sun (which takes a 
year in going once around), she overtakes and passes him at 



92 SIDEKEAL AND SYNODIC MONTHS. [§ 13 ^ 

regular intervals ; and as her phases depend upon her apparent 
position with reference to the su^ this interval from new- 
moon to new moon is specially noticeable, and is what we 
ordinarily understand as the " month." 

The angular distance of the moon east or west of the sun at 
any time is called her Elongation. At new moon it is zero, 
and the moon is said to be in Conjunction. At full moon the 
elongation is 180°, and she is said to be in Opposition. In 
either case the moon is in Syzygy. {Syzygy means. " yoked 
together," the sun, moon, and earth being then nearly in line.) 
When the elongation is 90°, she is said to be in Quadrature. 

133. Sidereal and Synodic Months. — The sidereal month is 
the time it takes the moon to make her revolution from a given 
star to the same star again ; its length is 27 \ days (27 days, 7 
hours, 43 minutes, 11.524 seconds). The mean daily motion, 
therefore, is 360° divided by this, or 13° 11' (nearly). The 
sidereal month is the true month from the mechanical point 
of view. 

The synodic month is the time between two successive con- 
junctions or oppositions; i.e., between two successive new or 
full moons. Its average length is about 29-J- days (29 days, 
12 hours, 44 minutes, 2.841 seconds), but it varies consider- 
ably on account of the eccentricity of the moon's orbit. 

If M be the length of the moon's sidereal period in days, E the 
length of the sidereal year, and S that of the synodic month, the three 

quantities are connected by a simple relation easily demonstrated. — 
is the fraction of a circumference moved over by the moon in a day. 

Similarly, — is the apparent daily motion of the sun. The difference 

E 
is the amount which the moon gains on the sun daily. Now it gains 
a whole revolution in one synodic month of S days, and therefore 

must gain daily — of a circumference. Hence we have the important 

S 
equation _I __ JL = .1 

M E 8 



§ 133] MOON'S PATH AMONG THE STABS. 93 

which is known as the equation of synodic motion. In a sidereal year 
the number of sidereal months is exactly one greater than the num- 
ber of synodic months, the numbers being respectively 13.369 + and 
12.369 +. 

134. The Moon's Path among the Stars. — By observing the 
moon's right ascension and declination daily with suitable 
instruments, we can map out its apparent path, just as in the 
case of the sun (Art. 116) . This path turns out to be (very 
nearly) a great circle, inclined to the ecliptic at an angle of 
5° 8'. The two points where it cuts the ecliptic are called the 
"nodes," the ascending node being where the moon passes 
from the south side to the north side of the ecliptic, while the 
opposite node is called the descending node. 

The moon at the end of the month never comes back exactly to the 
point of beginning among the stars, on account of the so-called " per- 
turbations" of her orbit, due mostly to the attraction of the sun. 
One of the most important of these perturbations is the " regression 
of the nodes." These slide westward on the ecliptic just as the vernal 
equinox does (precession), but much faster, completing their circuit 
in about 19 years instead of 26,000. 

135. Interval between the Moon's Successive Transits ; Daily 
Retardation. — Owing to the eastward motion of the moon it 
comes to the meridian about 51 minutes later each day, on 
the average ; but the retardation ranges all the way from 38 
minutes to 66 minutes, on account of the variation in the rate 
of the moon's motion. 

The average retardation of the moon's rising and setting is 
also, of course, the same 51 minutes ; but the actual retarda- 
tion is still more variable than that of the meridian transits, 
depending to some extent on the latitude of the observer as 
well as on the variations in the moon's motion. At New 
York the range is from 23 minutes to 1 hour and 17 minutes ; 
that is to say, on some nights the rising of the moon is only 
23 minutes later than on the preceding night, while at other 



94 HARVEST AND HUNTER'S MOON. [§ 135 

times it is more than an hour and a quarter behindhand. In 
high latitudes the differences are still greater. In very high 
latitudes the moon, when it has its greatest possible declina- 
tion, becomes circumpolar for a certain time each month, 
and remains visible without setting at all (like the midnight 
sun) for a greater or less number of days, according to the 
latitude of the observer. 

136. Harvest and Hunter's Moon. — The full moon that 
occurs nearest the autumnal equinox is called the < harvest 
moon ' ; the one next following, the 6 hunter's moon/ At that 
time of the year the moon, while nearly full, rises for several 
consecutive nights almost at the same hour, so that the moon- 
light evenings last for an unusually long time. The phenome- 
non, however, is much more striking in Northern Europe and 
in Canada than in the United States. 

137. Form of the Moon's Orbit. — By observation of the 
moon's apparent diameter in connection with observations of 
her place in the sky, we can determine the form of her orbit 
around the earth in the same way that the form of the earth's 
orbit around the sun was worked out (see Appendix, Art. 
428). The moon's apparent diameter ranges from 33' 33", 
when as near the earth as possible, to 29' 24", when most 
remote ; and her orbit turns out to be an ellipse like that of 
the earth around the sun, but of much greater eccentricity, 
averaging about -^ (as against -^). We say " averaging" be- 
cause the actual eccentricity is variable, on account of pertur- 
bations. 

The point of the moon's orbit nearest the earth is called the 
Perigee, that most remote the Apogee, and the indefinite line 
passing through these points the Line of Apsides, while the 
major axis is that portion of this line which lies between the 
perigee and apogee. This line of apsides is in continual 
motion, on account of perturbations (just as the line of nodes 



§ 137] THE MOON'S DISTANCE. 95 

is, Art. 134), but it moves eastward instead of westward, com- 
pleting its revolution in about nine years. In her revolution 
about the earth, the moon observes the same law of equal 
areas that the earth does in her orbit around the sun (Art. 
121). 

THE MOON'S DISTANCE. 

138. In the case of any heavenly body, one of the first and 
most fundamental inquiries relates to its distance from us : 
until the distance has been somehow measured we can get no 
knowledge of the real dimensions of its orbit, nor of the size, 
mass, etc., of the body itself. The problem is usually solved 
by measuring the apparent " parallactic " displacement of the 
body, as seen by observers at widely separated stations. 
Before proceeding farther, we must, therefore, say a few 
words upon the subject of parallax. 

139. Parallax. — In general the word " parallax" means 
the difference between the directions of a heavenly body as 
seen by the observer, and as seen from some standard point 
of reference. The annual or heliocentric parallax of a star is 
the difference of the star's direction as seen from the earth 
and from the sun. The diurnal or geocentric parallax of the 
sun, the moon, or a planet, is the difference between its direc- 
tion as seen from the centre of the earth and from the obser- 
ver's station on the earth's surface ; or, what comes to the same 
thing, the geocentric parallax is the angle at the body made by 
tivo lines drawn from it, one to the observer, the other to the centre 
of the earth. (Stars have no geocentric parallax; the earth as 
seen from them is a mere point.) 

In Tig. 17, the parallax of the body P is the angle OPC. 
Obviously this diurnal parallax is zero for a body directly over- 
head at Z, and is the greatest possible for a body on the hori- 
zon, as at P h . 



96 



PARALLAX AND DISTANCE. 



[§139 



Moreover, and this is to be specially noted, this parallax of 
a body at the horizon — the " horizontal parallax " — is simply 
the angular semi-diameter of the earth as seen from the body. 
When, for instance, we say that the moon's horizontal parallax 
is 57', it is equivalent to saying that seen from the moon the 
earth appears to have a diameter of 114'. In the same way, 
since the sun's parallax is 8".8, the diameter of the earth as 
seen from the sun is 17" '.6. 



140. Relation between Parallax and Distance. — When the 
horizontal parallax of any heavenly body is ascertained, its dis- 
tance follows at once through 
our knowledge of the earth's 
dimensions. If we know how 
large a ball of given size 
appears, we can tell how far 
away it is; if we know how 
large the earth looks from the 
moon, we can find the distance 
between them. Thus, when in 
the triangle CP h O, Fig. 17, we 
know the angle at P h , and the 
side CO, the radius of the 
earth, we can compute CP h by 
a very easy trigonometrical 
calculation. Evidently the more remote the body, the smaller 
its parallax. 

Since the radius of the earth varies slightly in different lati- 
tudes, we take the equatorial radius as a standard, and the 
equatorial horizontal parallax is the earth's equatorial semi- 
diameter as seen from the body. It is this which is usually 
meant when we speak simply of " the parallax " of the moon, 
of the sun, or of a planet without adding any qualification 
(but never when we speak of the parallax of a star ; then we 
always mean the annual parallax). 




Fig. 17. — Diurnal Parallax. 



§ 141] DIAMETER, ETC., OF THE MOON. 97 

141. Parallax, Distance, and Velocity of the Moon. — The 

moon's equatorial horizontal parallax found by corresponding 
observations made at different parts of the earth, is 3422" (57' 
2") according to Neison, but varies considerably on account of 
the eccentricity of the orbit. From this parallax we find 
that the moon's average distance from the earth is about 60.3 
times the earth's equatorial radius, or 238,840 miles, with an 
uncertainty of perhaps 20 miles. 

The maximum and minimum values of the moon's distance are 
given by Neison as 252,972 and 221,617 miles. It will be noted that 
the average distance is not the mean of the two extremes. 

Knowing the size and form of the moon's orbit, the velocity 
of her motion is easily computed. It averages a little less 
than 2300 miles an hour, or about 3350 feet per second. Her 
mean apparent angular velocity among the stars is about 33', 
which is just a little greater than the apparent diameter of 
the moon itself. 

142. Diameter, Area, and Bulk of the Moon. — The mean 
apparent diameter of the moon is 31' 7". Knowing its dis- 
tance, its real diameter comes out 2163 miles. This is 0.273 
of the earth's diameter. 

Since the surfaces of globes vary as the squares of their 
diameters, and their volumes as the cubes, this makes the sur- 
face area of the moon equal to about -^ of the earth's, and the 
volume (or bulk) almost exactly ^ of the earth's. 

No other satellite is nearly as large as the moon in comparison with 
its primary planet. The earth and moon together, as seen from a dis- 
tance, are really in many respects more like a double planet than like 
a planet and satellite of ordinary proportions. At a time, for instance, 
when Venus happens to be nearest the earth (at a distance of about 
twenty-five millions of miles), her inhabitants (if she has any) would 
see the earth considerably brighter than Venus herself at her best 
appears to us, and the moon would be about as bright as Sirius, oscil- 



98 MASS, DENSITY, ETC., OF THE MOON. [§ 143 

lating backwards and forwards about half a degree each side of the 
earth, once a month. 

143. Mass, Density, and Superficial Gravity of the Moon. 

— Her mass is about g 1 ^- of the earth's mass (0.0125). The 
actual measurement of the moon's mass is an extremely diffi- 
cult problem, and the methods pursued are quite beyond the 

"TV/Too o 

scope of this book. Since the density is equal to — , the 

Volume 

density of the moon as compared to that of the earth is found 
to be 0.613, or about 3.4 the density of water (the earth's 
density being 5.58). This is a little above the average den- 
sity of the rocks which compose the crust of the earth. 

The c superficial gravity/ or the attraction of the moon for 
bodies at its surface, is about one-sixth that at the surface of 
the earth. This is a fact that must be borne in mind in con- 
nection with the enormous scale of the craters on the moon. 
Volcanic forces there would throw materials to a vastly greater 
distance than on the earth. 

144. Rotation of the Moon. — The moon turns on its axis 
once a month, in exactly the time occupied by its revolution 
around the earth : its day and night are, therefore, each nearly 
a fortnight in length, and in the long run it keeps the same 

side always toward the earth. We see to- 
day precisely the same face of the moon 
I which Galileo did when he first looked at it 
with his telescope. The opposite face has 
never been seen from the earth, and prob- 
ably never will be. 



a 



V 



It is difficult for some to see why a motion of 

this sort should be considered a rotation of the 

moon, since it is essentially like the motion of a 

Fig. 18. ^n carried on a revolving crank (Fig. 18). Such 

a ball, they say, "revolves around the shaft, but does not rotate on 

its own axis." It does rotate, however ; for if we mark one side of 



§ 144] THE MOON'S PHASES. 99 

the ball, we shall find the marked side presented successively to every 
point of the compass as the crank turns around, so that the ball turns 
on its own axis as really as if it were whirling upon a pin fastened to 
the table. By virtue of its connection with the crank, the ball has 
two distinct motions, — (1) the motion of translation, which carries its 
centre in a circle around the shaft ; (2) an additional motion of rota- 
tion around a line drawn through its centre of gravity parallel to the 
shaft. 

Rotation consists essentially in this : A line connecting any two points 
in the rotating body, and produced to the celestial sphere, will sweep out a 
circle upon it. In every rotating body, one line can be drawn through 
the centre of the body, however, so that the circle described by it in 
the sky will be infinitely small. This is the axis of the body. 

145. Librations. — While in the long run the moon keeps the 
same face towards the earth, it is not so from day to day. With refer- 
ence to the centre of the earth, it is continually oscillating a little, 
and these oscillations constitute what are called " Librations," of 
which we distinguish three; viz., (1) the libration in latitude, by 
which the north and south poles are alternately presented to the earth ; 
(2) the libration in longitude, by which the east and west sides of the 
moon are alternately tipped a little towards us; and (3) the diurnal 
libration, which enables us to look over whatever edge of the moon is 
uppermost when it is near the horizon. Owing to these librations we 
see considerably more than half of the moon's surface at one time 
and another. About 41 per cent of it is always visible ; 41 per cent 
never visible, and a belt at the edge of the moon, covering about 18 
per cent is rendered alternately visible and invisible by libration. 

146. Phases of the Moon. — Sinc3 the moon is an opaque 
globe shining merely by reflected light, we can only see that 
hemisphere of her surface on which, the sun is shining, and of 
the illuminated hemisphere only that portion which happens 
to be turned towards the earth. 

When the moon is between the earth and the sun (new 
moon), the side presented to us is dark, and the moon is 
then invisible. A week later, at the end of the first quarter, 
half of the illuminated hemisphere is visible, and we have the 



100 



THE MOON'S PHASES. 



[§140 



half-moon just as we do a week after the full. Between the 
new moon and the half-moon, during the first and last quarters 
of the lunation, we see less than half of the illuminated por- 
tion, and then have the "crescent" phase. Between half- 
moon and the full moon, during the second and third quarters 




Fig. 19. — The Moon's Phases. 

of the lunation, we see more than half of the moon's illumi- 
nated side, and we have then what is called the "gibbous" 
phase. 

Fig. 19 (in which the light is supposed to come from a point far 
above the circle which represents the moon's orbit) shows the way in 
which the phases are distributed through the month. 



§ 146] EARTH-SHINE ON THE MOON. 101 

The line which separates the dark portion of the disc from 
the bright is called the Terminator, and is always a semi- 
ellipse, since it is a semicircle viewed obliquely, as shown by 
Fig. 20, A. Draughtsmen sometimes incorrectly represent the 
crescent form by a construction like Fig. 20, B, in which a 
smaller circle has a portion cut out of it by an arc of a larger 
one. It is to be noticed also that ab, 
the line which joins the " cusps " or /T\\ /^V\ 

points of the crescent, is always perpen- 1<(J \ c ]fi ( I ) 

dicular to a line drawn from the moon \\ j / \^ J J 

to the sun, so that the horns are always b 

turned directly away from the sun. The A 

precise position in which they will stand 

at any time is, therefore, perfectly predictable, and has nothing 

whatever to do with the weather. (Pupils have probably 

heard of the " wet moon " and " dry moon " superstition.) 

147. Earth-shine on the Moon. — Near the time of new 
moon, the portion of the moon's disc which does not get the 
sunlight is easily visible, illuminated by a pale reddish light. 
This light is earth-shine, — the earth as seen from the moon 
being then nearly full. The red color is due to the fact that 
the light sent to the moon from the earth has passed twice 
through our atmosphere, and so has acquired the sunset tinge. 
Seen from the moon, the earth would be itself a magnificent 
moon about 2° in diameter, showing the same phases as the 
moon does itself. 

Taking everything into account, the earth-shine is probably fifteen 
to twenty times as strong as the light of the moon at similar phases. 
Since the moon keeps always the same face towards the earth, the 
earth is visible only from that part of the moon which faces us, and 
remains nearly stationary in the lunar sky, neither rising nor setting. 
It is easy to see that she w r ould be a very beautiful object, on account 
of the changes which would be continually going on upon her surface 
due to snow-storms, clouds, growth of vegetation, etc. 



102 ABSENCE OF AIR AND WATER. [§ 148 

PHYSICAL CHARACTERISTICS OF THE MOON. 

148. Absence of Air and Water. — The moon's atmosphere, 
if there is any, is extremely rare, its density at the moon's 
surface being probably not more than 10 1 00 part of that of our 
own atmosphere. 

The evidence on the point is twofold: First, the telescopic appear- 
ance. There is no haze, shadows are perfectly black; there is no 
sensible twilight at the points of the crescent, and all outlines are visi- 
ble sharply and without the least blurring such as would be due to 
the intervention of an atmosphere. Second, the absence of refraction 
when the moon intervenes between us and any distant body. When 
the moon c occults ' a star, for instance, there is no distortion or dis- 
coloration of the star-disc, but both the disappearance and the reap- 
pearance are practically instantaneous. 

Of course if there is no air, there can be no liquid water, 
since the water would immediately evaporate and form an 
atmosphere of vapor if air were not present. It is not impos- 
sible, however, nor perhaps improbable, that solid water (ice 
and snow) may exist on the moon's surface. Although ice and 
snow liberate a certain amount of vapor, yet at a low temper- 
ature the quantity would be insufficient to make an atmos- 
phere dense enough to be observed from the earth. 

If the moon once formed a portion of the earth, as is likely, 
the absence of air and water requires explanation, and there 
have been many interesting speculations on the subject into 
which we cannot enter. 

149. The Moon's Light. — In its quality moonlight is simply 
sunlight, showing a spectrum identical in every detail with 
that of the light coming from the sun itself, except as the 
intensity of different portions of the spectrum is slightly 
altered by its reflection from the lunar surface. 

The brightness of full moonlight as compared with sunlight 
is about one six-hundred-tlwusandth. According to this, if the 



§ 149] HEAT OF THE MOON. 103 

whole visible hemisphere were packed with full moons, we 
should receive from it only about one-eighth of the light of the 
sun. 

The half-moon does not give nearly half as much light as 
the full moon. Near the full the brightness is suddenly and 
greatly increased, probably because at any time except the 
full the moon's visible surface is more or less darkened by 
shadows which disappear at the moment of full. 

The average "albedo," or reflecting power, of the moon's 
surface is given by Zollner as 0.174; i.e., the moon's surface 
reflects a little more than one-sixth of the light that falls 
upon it. There are, however, great differences in the bright- 
ness of the different portions of the moon's surface. Some 
spots are nearly as white as snow or salt, and others as dark 
as slate. 

150. Heat of the Moon. — For a long time it was impossible 
to detect the moon's heat by observation. Even when concen- 
trated by a large lens, it is too feeble to be shown by the most 
delicate thermometer. With modern apparatus, however, it is 
easy enough to perceive the heat of lunar radiation, though the 
measurement is extremely difficult. The total amount of heat 
sent by the full moon to the earth appears to be about -pnnnnr °^ 
that sent by the sun; i.e., the full moon in two days sends 
us about as much heat as the sun does in one second. 

A considerable portion of the lunar heat seems to be simply 
reflected from the surface like light, while the rest, perhaps 
three-fourths of the whole, is "obscure heat"; i.e., heat which 
has first been absorbed by the moon's surface and then radi- 
ated, like the heat from a brick surface that has been warmed 
by the sunshine. 

As to the temperature of the moon's surface, it is impossible 
to be very certain. During the long lunar night of fourteen 
days, the temperature must inevitably fall appallingly low, 
— perhaps 200° or 300° below zero. On the other hand, the 



104 LUNAR INFLUENCES. [§ 150 

lunar rocks are exposed to the sun's rays in a cloudless sky 
for fourteen days at a time, so that if they were protected by 
air, like the rocks upon the earth, they would certainly become 
intensely heated. But there is no air, and, on the whole, it is 
probable that the temperature never rises much above the 
freezing-point of water, since in the absence of air the heat 
would be lost about as fast as it is received, and the condition 
of things may be supposed to be somewhat like that on the 
highest mountains of the earth (where there is perpetual snow 
and ice), only more so. 

151. Lunar Influences on the Earth. — The most important 
effect produced upon the earth by the moon is the generation 
of the tides in co-operation with the sun. There are also cer- 
tain well-ascertained disturbances of the terrestrial magnetism 
connected with the approach and recession of the moon in its 
oval orbit; and this ends the chapter of proved lunar influ- 
ences. 

The multitude of current beliefs as to the controlling influ- 
ence of the moon's phases and changes upon the weather and 
the various conditions of life are mostly unfounded. It is 
quite certain that if the moon has any influence at all of the 
sort imagined, it is extremely slight ; so slight that it has not 
yet been demonstrated, though numerous investigations have 
been made expressly for the purpose of detecting it. Different 
workers continually come to contradictory results. 

152. The Moon's Telescopic Appearance. — Even to the 
naked eye the moon is a beautiful object, diversified with curi- 
ous markings connected with numerous popular legends. In 
a powerful telescope these naked-eye markings vanish, and 
are replaced by a multitude of smaller details which make the 
moon, on the whole, the most interesting of all telescopic 
objects — especially to instruments of moderate size, say from 
six to ten inches in diameter, which generally give a more 



§152] 



THE MOON S SURFACE. 



105 



pleasing view than instruments either much larger or much 
smaller. An instrument of this size, with magnifying powers 
between 250 and 500, virtually brings the moon within a dis- 
tance ranging from 1000 to 500 miles. Any object half a 
mile in diameter on the moon is distinctly visible. A long 
line or streak even less than a quarter of a mile across can 
easily be seen. 

For most purposes the best time to look at the moon is when it is 
between six and ten days old : at the time of full moon few parts of 
the surface are well seen. It is evident that while with the telescope 
we should be able to see such objects as lakes, rivers, forests, and 
great cities, if they existed on the moon, it would be hopeless to 
expect to distinguish any of the minor indications of life, such as 
buildings or roads. 

153. The Moon's Surface Structure. — The moon's surface 
for the most part is extremely broken. The earth's mountains 
are mainly in long ranges, like the Andes and Himalayas. * 
On the moon the ranges are few in number ; but, on the other 
hand, the surface 
is pitted all over 
with great craters, 
which resemble 
very closely the 
volcanic craters on 
the earth's surface, 
though on an im- 
mensely greater 
scale. The largest 
terrestrial craters 

do not exceed six or seven miles in diameter ; many of those 
on the moon are fifty or sixty miles across, and some have a 
diameter of more than a hundred miles, while smaller ones 
from five to twenty miles in diameter are counted by the 
hundred. 

The normal lunar crater (Fig. 21) is nearly circular, sur- 




Fig. 21. — A Normal Lunar Crater (Nasmyth). 



106 



LUNAR CRATERS AND MOUNTAINS. 



[§153 



rounded by a mountain ring, which rises anywhere from 1000 
to 20,000 feet above the neighboring country. The floor within 
the ring may be either above or below the outside level ; some 
craters are deep, and some are filled nearly to the brim. Fre- 
quently, in the centre of the crater, there rises a group of 
peaks which attain the same elevation as the encircling ring, 
and these central peaks often show holes or minute craters 
in their summits. 

On some portions of the moon these craters stand very 
thickly. This is especially the case near the moon's south 

pole. It is noticeable, 
also, that as on the 
earth the youngest 
mountains are gener- 
ally the highest, so on 
the moon the most re- 
cent craters are gener- 
ally deepest and most 
precipitous. 

The height of a lu- 
nar mountain can be 
measured with consid- 
erable accuracy by 
means of its shadow. 

The striking resem- 
blance of these lunar 
craters to terrestrial vol- 
canoes makes it natural 
to assume that they have 
a similar origin. This, 
however, is not quite certain, for there are considerable difficulties in 
the way of the volcanic theory, especially in the case of what are 
called the great " Bulwark Plains," so extensive that a person stand- 
ing in the centre could not even see the summit of the surrounding 
ring at any point; and yet there is no line of distinction between 
them and the smaller craters, — the series is continuous. Moreover, 




Fig. 22. — Gassendi (Nasmyth). 



§153] 



OTHER LUNAR FORMATIONS. 



107 



on the earth, volcanoes necessarily require the action of air and water, 
which do not now exist on the moon ; so that if these lunar craters 
are really the result of volcanic eruptions, they must be ancient forma- 
tions, for there is absolutely no evidence of any present volcanic 
activity. Fig. 22 represents one of the finest lunar craters,' Gassendi, 
which is best seen about two days after the half moon. 

154. Other Lunar Formations. — The craters and mountains 
are not the only interesting features on the moon's surface. 
There are many deep, narrow, crooked valleys which go by the 
name of "rills/' and 
may once have been 
water-courses (see Fig. 
23). Then there are 
many straight " clefts " 
half a mile or so wide, 
and of unknown depth, 
running in some cases 
several hundred miles 
straight through moun- 
tain and valley, with- 
out any apparent re- 
gard for the accidents 
of the surface. 

Most curious of all 
are the light-colored 
streaks, or "rays/' 
which, radiate from cer- 
tain of the craters, ex- 
tending in some cases 
a distance of many hundred miles. They are usually from five 
to ten miles wide, and neither elevated nor depressed to any 
considerable extent with reference to the general surface. 
Like the clefts;, they pass across valley and mountain, and 
sometimes straight through craters, without any change in 
width or color. No satisfactory explanation of them has yet 




Fig. 23. — Archimedes and the Apennines (Nasmyth). 



108 



MAP OF THE MOON. 



[§154 



been given. The most remarkable of these " ray-systems " is 
the one connected with the great crater Tycho, not very far 
from the moon's south pole. The rays are not very conspic- 
uous until within a few days of full moon, but at that time 
they, and the crater from which they diverge, constitute by 
far the most striking feature of the telescopic view. 







Fig. 24. — Map of the Moon, reduced from Neison. 

155. Changes on the Moon. — It is certain that there are 
no conspicuous changes on the moon's surface ; no such trans- 
formations as would be presented by the earth viewed with a 
telescope from the moon, — no clouds, no storms, no snow of 



§ 155] 



CHANGES ON THE MOON. 



109 



winter, and no spread of verdure in the spring. At the same 
time it is confidently maintained by some observers that here 
and there alterations do take place in the details of the lunar 
surface, while others as stoutly dispute it. The difficulty in 
settling the question arises from the great changes which take 
place in the appearance of a lunar object, according to the 
angle at which the sunlight strikes it. Other conditions also, 
such as the height of the moon above the horizon and the 
clearness and steadiness of the air, affect the appearance ; and 
it is very difficult to secure a sufficient identity of conditions 
at different times of observation to be sure that apparent 
changes are real. It is probable that the question will finally 
be settled by photography. For further discussion of this 
subject, see General Astronomy, Art. 272. 



KEY TO THE PRINCIPAL OBJECTS INDICATED IN FIG. 24. 



A. Mare Humorum. 




K. 


Mare Nubium. 


B. Mare Nectaris. 




L. 


Mare 


Frigoris. 


C. Oceanus Procellarum. 


T. 


Leibnitz Mountains. 


D. Mare Fecunditatis. 




U. 


Doerfel Mountains. 


E. Mare Tranquilitatis. 


V. 


Rook Mountains. 


F. Mare Crisium. 




W. 


DAlembert Mountains. 


G. Mare Serenitatis. 




X. 


Apennines. 


H. Mare Imbrium. 




Y. 


Caucasus. 


/. Sinus Iridum. 




Z. 


Alps. 




1. Clavius. 


14. 


Alphonsus. 




27. Eratosthenes 


2. Schiller. 


15. 


Theophilus. 




28. Proclus. 


3. Maginus. 


16. 


Ptolemy. 




28'. Pliny. 


4. Schickard. 


17. 


Langrenus. 




29. Aristarchus. 


5. Tycho. 


18. 


Hipp arch us. 




30. Herodotus. 


6. Walther. 


19. 


Grimaldi. 




31. Archimedes. 


7. Purbach. 


20. 


Flam steed. 




32. Cleomedes. 


8. Petavius. 


21. 


Messier. 




33. Aristillus. 


9. "The Railway." 


22. 


Maskelyne. 




34. Eudoxus. 


10. Arzachel. 


23. 


Triesnecker. 




35. Plato. 


11. Gassendi. 


24. 


Kepler. 




36. Aristotle. 


12. Catherina. 


25. 


Copernicus. 




37. Endymion. 


13. Cyrillus. 


26. 


Stadius. 







110 NOMENCLATURE. [§ 156 

156. Lunar Maps and Nomenclature. — A number of maps 
of the moon have been constructed by different observers. 
The most recent and extensive is that by Schmidt of Athens, 
on a scale of seven feet in diameter ; it was published by the 
Prussian government in 1878. Perhaps the best for ordinary 
observers is that given in Webb's u Celestial Objects for Com- 
mon Telescopes." We present here (Fig. 24) a skeleton map, 
which indicates the position of about fifty of the leading 
objects. 

As for the names of the lunar objects, the great plains upon 
the surface were called by Galileo " oceans," or " seas " (Maria), 
because he supposed that these grayish surfaces, which are 
visible to the naked eye and conspicuous in a small telescope, 
though not with a large one, were covered with water. Thus we 
have the "Oceanus Procellarum " (Sea of Storms), the "Mare 
Imbrium" (Sea of Showers), etc. The ten mountain ranges 
on the moon are mostly named for terrestrial mountains, as 
Caucasus, Alps, Apennines, though two or three bear the 
names of astronomers, like Leibnitz, Poerfel, etc. The con- 
spicuous craters bear the names of ancient and mediaeval 
astronomers and philosophers, as Plato, Archimedes, Tycho, 
Copernicus, Kepler, and Gassendi. This system of nomencla- 
ture seems to have originated with Eiccioli, who made the first 
map of the moon in 1650. 

156* The first successful photographs of the moon were 
made by Eutherfurd of New York about 1866, and have 
remained unsurpassed until very recently. 

At present the Paris and Lick observatories are taking the 
lead, and producing negatives unprecedented in size and clear- 
ness. The plates constitute a permanent and unimpeachable 
record of the state of the lunar surface, which will soon settle 
the question of changes upon it ; and they supply the material 
for a much more perfect map of our satellite. 



§ 157] THE SUN. Ill 



CHAPTER VI. 

THE SUN. — ITS DISTANCE, DIMENSIONS, MASS, AND DEN- 
SITY. — ITS ROTATION, SURFACE, AND SPOTS. — THE 
SPECTROSCOPE AND THE CHEMICAL CONSTITUTION OF 
THE SUN. — THE CHROMOSPHERE AND PROMINENCES. 
— THE CORONA. — THE SUN'S LIGHT. — MEASUREMENT 
AND INTENSITY OF THE SUN'S HEAT. — THEORY OF ITS 
MAINTENANCE AND SPECULATIONS REGARDING THE 
AGE OF THE SUN. 

157. The sun is a star, — the nearest of them; a hot, self- 
luminous globe, enormous as compared with the earth and 
moon, though probably only of medium size as a star ; but to 
the earth and the other planets which circle around it, it is 
the grandest and most important of all the heavenly bodies. 
Its attraction controls their motions, and its rays supply the 
energy which maintains every form of activity upon their 
surfaces. 

158. The Sun's Distance. — The mean distance of the sun 
from the earth (the astronomical unit of distance) is a little 
less than 93,000000 miles. There are many methods of deter- 
mining it, some of which depend on a knowledge of the Ve- 
locity of Light (Appendix, Arts. 434 and 436), while others 
depend on finding the sun's horizontal parallax. (For a 
resume of the subject, see General Astronomy, Chap. XIV.) 
The mean value of this parallax is very nearly 8".8. In other 
words, as seen from the sun, the earth has an apparent diam- 
eter of about 17".6 (Art. 139). The distance is variable, to 



112 DIMENSIONS OF THE SUN. [§ 158 

the extent of about 1,500000 miles, on account of the eccen- 
tricity of the earth's orbit, the earth being almost 3,000000 
miles nearer to the sun on Dec. 31st than on July 1st. 

Knowing the distance of the earth from the sun, the earth's 
orbital velocity follows at once by dividing the circumference 
of the orbit by the number of seconds in a year. It comes out 
18.5 miles per second. (Compare this with the velocity of a 
cannon-ball, which seldom exceeds 2500 feet per second.) In 
travelling this 18^- miles, the deflection of the earth's motion from 
a perfectly straight line amounts to less than one-ninth of an inch. 

159. The distance of the sun is of course enormous compared with 
any distance upon the earth's surface. Perhaps the simplest illustra- 
tion which will give us any conception of it is that drawn from the 
motion of a railway train, which, going a thousand miles a day 
(nearly forty-two miles an hour without stops) would take 254J years 
to make the journey. If sound were transmitted through interplan- 
etary space, and at the same rate as in our own air, it would make the 
passage in about fourteen years ; i.e., an explosion on the sun would 
be heard by us fourteen years after it actually occurred. Light trav- 
erses the distance in 499 seconds. 

160. Dimensions of the Sun. — The sun's mean apparent 
diameter is 33' 4". Since at its distance, 1" equals 450.36 
miles, its diameter is 866,500 miles, or 109^- times that of the 
earth. If we suppose the sun to be hollowed out, and the 
earth placed at the centre of it, the sun's surface would be 
433,000 miles away. Now since the distance of the moon 
from the earth is about 239,000 miles, she would be only 
a little more than half-way out from the earth to the inner 
surface of the hollow globe, which would thus form a very 
good background for the study of the lunar motions. 

If we represent the sun by a globe two feet in diameter, the earth on 
the same scale would be 0.22 of an inch in diameter, the size of a very 
small pea. Its distance from the sun would be just about 220 feet, 
and the nearest star, still on the same scale, would be 8000 miles away, 
on the other side of the earth. 



§ 160] sun's mass, density, etc. 113 

Since the surfaces of globes are proportional to the squares 
of their radii, the surface of the sun exceeds that of the earth 
in the ratio of (109.5) 2 : 1 ; i.e., the area of its surface is about 
12,000 times the surface of the earth. 

The volumes of spheres are proportional to the cubes of 
their radii, hence the sun's volume or bulk is (109. 5) 3 , or 
1,300000 times that of the earth. 

161. The Sun's Mass, Density, and Superficial Gravity. — 

The mass of the sun is nearly 332,000 times that of the earth. 
There are various ways of getting at this result, but they lie 
rather beyond the mathematical scope of this work. 

Its density, as compared with that of the earth, is found by 
simply dividing its mass by its bulk (both as compared with the 

earth) ; i.e., the sun's density equals - = 0.255, — a 

. J * 1,300000 

little more than a quarter of the earth's density. 

To get its 'specific gravity' (i.e., its density compared with 
water), we must multiply this by the earth's mean specific 
gravity, 5.58. This gives 1.41. In other words, the sun's 
mean density is only about 1.4 times that of water, a very 
significant result as bearing on its physical condition, espe- 
cially when we know that a considerable portion of its mass is 
composed of metals. 

Of course this low density depends upon the fact that the tempera- 
ture is enormously high, and the materials are mainly in a state of 
cloud, vapor, or gas. 

The superficial gravity is about 27.6 as great as gravity on 
[the earth ; that is to say, a body which weighs one pound on 
the surface of the earth would there weigh 27.6 pounds, and 
a person who weighs 150 pounds here would there weigh 
nearly two tons. A body would fall 444 feet in the first 
second, and a pendulum which vibrates seconds on the earth 
would vibrate in less than a fifth of a second there. 



114 



THE SUNS ROTATION. 



[§162 



162. The Sun's Rotation. — Dark spots are often visible 
upon the sun's surface, which pass across the disc from east 

to west and indicate an axial 
rotation. The average time 
occupied by a spot in passing 
around the sun and return- 
ing to the same apparent po- 
sition, as seen from the earth, 
is 27.25 days. This interval, 
however, is not the true time 
of the sun's rotation, but the 
synodic, as is evident from 
Fig. 25. Suppose an obser- 
ver on the earth at E sees a 
spot on the centre of the 




Fig. 25. 



Synodic and Sidereal Revolutions of the Sun. sun's disc at S ; while the 

sun rotates, E will also move forward in its orbit, and the 
observer, the next time he sees the spot on the centre of the 
disc, will be at E 1 , the spot having gone around the whole 
circumference plus the arc SS'. 

The equation by which the true period is deduced from the synodic 
is the same as in the case of the moon ; viz., 

1=1- L 

S T E' 

T being the true period of the sun's rotation, E the length of the year, 
and 5 the observed synodic rotation. This gives T— 25.35. Differ- 
ent observers get slightly different results. 

The paths of the spots across the sun's disc are usually more 
or less oval, showing that the sun's axis is inclined to the 
ecliptic, and so inclined that the north polo is tipped about 
7\° towards the position which the earth occupies near the 
first of September. Twice a year the paths become straight, 
when the earth is in the plane of the sun's equator, June 3d 
and Dec. 5th (Fig. 26). 



§ 163] LAW OF THE SUN'S ROTATION. 115 

163. Peculiar Law of the Sun's Rotation. — It was noticed 
quite early that different spots give different results for the 





Fig. 26. — Path of Spots across the Sun's Disc. 

period of rotation, but the researches of Carrington, about 
forty years ago, first brought out the fact that the differences 
are systematic, so that at the solar equator the time of solar 
rotation is less than on either side of it. For spots near the 
sun's equator it is about 25 days ; for solar latitude 30°, 
26.5 days j and in solar latitude 40°, 27 days. The time of 
rotation of the sun's surface in latitude 45° is fully two days 
longer than at the equator ; but we are unable to follow the 
law further towards the poles of the sun, because spots are 
almost never found beyond the parallel of 45°. ]STo really 
satisfactory explanation of this strange acceleration of the 
spots at the sun's equator has yet been found. 

164. Study of the Sun's Surface. — The heat and light of 
the sun are so intense that we cannot look directly at it with 
a telescope, as we do at the moon, 
and it is necessary, therefore, to 
provide either a special eye-piece 
with suitable shade-glass, or arrange 
the telescope, as in Fig. 27, so as to 
throw an image of the sun upon a 
screen. 

In the study of the sun's surface, 

photography is for Some purposes Fig. 27. -Telescope and Screen. 

very advantageous and much used. The instrument must, 
however, have lenses specially constructed for photographic 




116 



GREAT SUN SPOT. 



[§164 



operations, since an object-glass which would give admirable 
results for visual purposes would be worthless photograph- 




Fig. 28.— The Great Sun Spot of September, 1870, and the Structure of the Photo- 
sphere. From a Drawing by Professor Langley. From the " New Astronomy," by 
permission of the Publishers. 

ically. Since 1890, however, a few object glasses have been 
made with new kinds of glass, which are said to be good both 
for photography and for the eye. The exposure required to 
form a photographic picture is practically instantaneous. 
The negatives are usually from two inches up to eight or ten 



§ 164] THE PHOTOSPHERE. 117 

inches in diameter, and some of the best of them bear 
enlarging up to forty inches. 

Photographs have the great advantage of freedom from preposses- 
sion on the part of the observer, and in an instant of time they secure 
a picture of the whole surface of the sun such as would require a skil- 
ful draughtsman hours to copy. But, on the other hand, they take no 
advantage of the instants of fine seeing, but represent the solar sur- 
face as it happened to appear at the moment when the plate was 
uncovered, affected by all the momentary distortions due to atmos- 
pheric disturbances. 

165. The Photosphere. — The sun's surface seen with a tele- 
scope, under a medium magnifying power, appears to be of 
nearly uniform texture, though distinctly darker at the edges, 
and usually marked here and there with certain dark spots. 
With a higher power it is evident that the visible surface 
(called the photosphere) is by no means uniform, but is made 
up, as shown in Fig. 28, of a comparatively darkish background 
sprinkled over with grains, or " nodules," as Herschel calls 
them, of something more brilliant, — "like snowflakes on a 
gray cloth," according to Langley. These nodules or "rice- 
grains" are from 400 to 600 miles across, and, when the seeing 
is best, themselves break up into more minute "granules." For 
the most part, the nodules are about as broad as they are long, 
though of irregular form; but here and there, especially in 
the neighborhood of the spots, they are drawn out into long 
streaks, known as "filaments," "willow leaves," or "thatch 
straws." 

Certain bright streaks called " f aculse " are also usually visi- 
ble here and there upon the sun's surface, and though not very 
obvious near the centre of the disc, they become conspicuous 
near the " limb," or edge of the disc, especially in the neigh- 
borhood of the spots, as shown in Fig. 29. These faculse are 
probably of the same material as the rest of the photosphere, 
but elevated above the general level and intensified in bright- 



118 



THE PHOTOSPHERE. 



[§ 165 



ness. When one of them passes off the edge of the disc, it is 
sometimes seen as a little projection. The fact, however, that 
their spectrum shows bright lines of calcium vapor, makes it 
uncertain whether they may not be clouds of that substance 
floating high above the photosphere. 

In their nature, the photospheric "nodules " and faculse are 
in all probability luminous clouds, floating in a less luminous 
atmosphere, just as a snow or rain-cloud, which has been 




Fig. 29. — Faculse at Edge of the Sun (De La Rue). 

formed by the condensation of water-vapor, floats in the earth's 
atmosphere. Such a cloud, while at a temperature even lower 
than that of the surrounding gases, has a vastly greater power 
of emitting light, and therefore appears very brilliant in com- 
parison with the gas in which it floats, like the "mantle " of 
a Welsbach gas-burner. There is considerable probability 
that the principal element in the photosphere is Carbon, 
though this cannot yet be regarded as proved. 



§ 166] SUN SPOTS. 119 

166. Sun Spots. — Sun spots, whenever visible, are the most 
interesting and conspicuous objects upon the solar surface. 
The appearance of a normal sun spot (Fig. 30), fully formed 
and not yet beginning to break up, is that of a dark central 
"umbra," more or less circular, with a fringing "penumbra" 
composed of converging filaments. The umbra itself is not 
uniformly dark throughout, but is overlaid with filmy clouds, 




Fig. 30. — A Normal Sun Spot (Secchi; modified). 

which usually are rather hard to see, but sometimes are con- 
spicuous, as in the figure. Usually, also, within the umbra 
there are a number of round and very black spots, sometimes 
called "vortices," but often referred to as " Dawes's holes," 
after the name of their first discoverer. 

Even the darkest portions of the umbra, however, are dark 
only by contrast. Photometric observations show that ^he 
nucleus of a spot gives about one per cent as much light as 
a corresponding a^ea of the photosphere ; the blackest portion 
of a sun spot is really more brilliant than a calcium light. 



120 SUN SPOTS. [§ 166 

Very few spots are strictly normal. Frequently the umbra 
is out of the centre of the penumbra, or has a penumbra on 
one side only, and the penumbral filaments, instead of con- 
verging regularly towards the nucleus, are often distorted in 
every conceivable way. Spots are often gathered in groups 
within a common penumbra, separated from each other by 
brilliant " bridges," which extend across from the outside 
photosphere. Occasionally a spot has no penumbra at all, 
and sometimes we have what are called "veiled" spots, in 
which there seems to be a penumbra without any central 
nucleus. 

167. Nature of Sun Spots. — The spots are probably shallow 
depressions or hollows in the photosphere filled with gases and 
vapors which are cooler than the surrounding regions, and 
therefore absorb a considerable portion of light, and make the 
spot look dark. The evidence that they are depressions con- 
sists in the change in their appearance as they approach the 
"limb," or edge of the disc. Here the penumbra becomes 
wider on the outer edge, and narrower on the inner edge, and 
just before the spot goes out of sight around the edge of the 
sun, the penumbra on the inner edge entirely disappears. 
The appearance is precisely such as would be shown by a 



Fig. 31. — Sun Spots as Cavities. 



saucer-shaped cavity in the surface of a globe, the bottom of 
the cavity being painted black to represent the umbra, and 
the sloping sides gray for the penumbra (see Fig. 31). 



§ 167] DIMENSIONS OF SUN SPOTS. 121 

Observations upon a single spot would hardly be sufficient to 
prove this, because the spots are so irregular in their form ; but by 
observing the behavior of several hundred, the truth appears in the 
average result, Occasionally when a very .large spot passes off the 
sun's limb, a depression can be seen with the telescope. It is only 
fair to add, however, that some observers of great experience still 
dispute the received theory, and maintain that spots are dark clouds 
of some kind floating on, or just above, the photosphere. 

That the nucleus of a spot is generally cooler as well as 
darker than the rest of the sun's surface, has been proved by 
several observers by direct experiments, though very near the 
edge of the sun the reverse has been found to be the case in 
some instances. 

The penumbra is usually composed of u thatch straws/' or 
long drawn out filaments, and these, as has been said, con- 
verge in a general way towards the centre of the spot. In the 
neighborhood of the spot, the surrounding photosphere is 
usually much disturbed and elevated into faculae. 

168. Dimensions of Sun Spots, etc. — The diameter of the 
umbra of a sun spot varies all the way from 500 miles, in the 
case of a very small one, to 50,000 miles in the case of a very 
large one. The penumbra surrounding a group of spots is 
sometimes 150,000 miles across, though that is an exceptional 
size. Quite frequently sun spots are large enough to be visi- 
ble with the naked eye, and can actually be thus seen at sun- 
set or through a fog, or by the help of a simple colored glass. 
The depth of the bottom of a spot is very difficult to deter- 
mine, but according to Faye, Carrington, and some others, it 
seldom exceeds 2500 miles, and more often is between 500 and 
1500. 

The duration of sun spots is very various, but they are 
always short-lived phenomena from the astronomical point of 
view, sometimes lasting only for a few days, though more fre- 
quently for a month or two. In one instance a spot group 
attained the age of eighteen months. 



122 INFLUENCE OF SUN SPOTS. [§ 168 

Very little can be said as to their cause. Numerous theo- 
ries, more or less satisfactory, have been proposed. On the 
whole, perhaps the most probable view is that they are the 
effect of eruptions. It is not likely, however, that they are 
the holes or craters through which the eruptions break out, as 
Secchi at one time thought, and as Mr. Proctor maintained to 
the very last : it is more probable, in accordance with Secchi's 
later views, that when an eruption takes place, a hollow, or 
sink, results in the photospheric cloud-surface somewhere near 
it, in which hollow the cooler gases and vapors collect. It is 
almost universally admitted that in some way they are due to 
matter descending from above upon the photosphere, but 
there is wide difference of opinion as to the nature and source 
of the falling substance, — whether it is meteoric, or was 
formed by condensation in the upper regions of the solar 
atmosphere ; or thrown up from the photosphere by eruprtion, 
as the text suggests. 

169. Distribution of Spots, and their Periodicity. — It is a 

significant fact that the spots are confined mostly to two 
zones of the sun's surface between 5° and 40° of north and 
south solar latitude. Practically none are ever found beyond 
the latitude of 45°, but at the time when spots are most 
numerous, a few are found near the equator. In 1843 
Schwabe of Dessau, by the comparison of an extensive series 
of observations covering nearly twenty years, showed that 
the sun spots are probably periodic, being at some times much 
more numerous than at others, with a roughly regular recur- 
rence every ten or eleven years. A few years later he fully 
established this remarkable result. Wolf of Zurich has col- 
lected all the observations discoverable, and has obtained a 
pretty complete record back to 1610, when Galileo first dis- 
covered these objects. The average period is 11.1 years, but 
the maxima are somewhat irregular, both in time and as to 
the extent of the surface covered by spots. The last maxi- 
mum occurred in 1892-3. During the maximum the sun is 



§ 169] INFLUENCE OF SUN SPOTS. 123 

never free from spots, from 25 to 50 being frequently visible 
at once. During the minimum, on the contrary, weeks and 
even months pass without the appearance of a single one. 
The cause of this periodicity is not yet known. 

Another curious and important fact has recently been brought out 
by Spoerer, though not yet explained. Speaking broadly, the distur- 
bance which produces the spots of a given period first manifests 
itself in two belts, about 30° north and south of the sun's equator. 
These belts then draw in towards the equator, and the spot-maximum 
occurs when their latitude is about 10°; while the disturbance finally 
dies out at a latitude of from 5° to 10°, about twelve or fourteen 
years after its first outbreak. Two or three years before this dis- 
appearance, however, two new zones of disturbance show themselves. 
Thus at the spot-minimum there are usually four well marked spot- 
belts; two near the sun's equator, due to the expiring disturbance, 
and two in high latitudes, due to the newly beginning outbreak. 

170. Terrestrial Influence of Sun Spots. — One influence of 
sun spots on the earth is perfectly demonstrated. When the 
spots are numerous, magnetic disturbances {magnetic storms) 
are most numerous and most violent upon the earth — a fact 
not to be wondered at, since notable disturbances upon the 
sun's surface have been immediately followed by magnetic 
storms with brilliant exhibitions of the Aurora Borealis, as in 
1859 and 1883. But no one has yet been able to explain the 
nature of the connection by which disturbances upon the sun's 
surface affect the magnetic condition of the earth, though the 
fact is beyond doubt. 

It has been attempted, also, to show that the periodical disturbance 
of the sun's surface is accompanied by effects upon the earth's mete- 
orology, — upon its temperature, barometric pressure, storminess, and 
the amount of rain-fall. On the whole, it can only be said that while 
it is possible that real effects are produced, they must be very slight, 
and are almost entirely covered up by the effect of purely terrestrial 
causes. The results obtained thus far in attempting to co-ordinate 
sun-spot phenomena with meteorological phenomena are unsatisfac- 



124 THE SOLAR SPECTRUM. [§ 170 

tory and often contradictory. We may add that the spots cannot 
produce any sensible effect by their direct action in diminishing the 
light and heat of the sun. They do not directly alter the amount of 
solar radiation at any time by so much as one part in a thousand. 

THE SOLAR SPECTRUM AND ITS REVELATIONS. 

About 1860 the spectroscope appeared in the field as a new 
and powerful instrument for astronomical research, resolving 
at a glance many problems which before did not seem even 
open to investigation. 

171. Principle of the Spectroscope. — The essential part of 
the apparatus is either a prism or a train of prisms, or else a 
diffraction "grating," 1 which is capable of performing the 
same office of " dispersing " (i.e., of spreading and sending in 
different directions) the light rays of different colors. 

If with such a " dispersion piece," as we may call it (either 
prism or grating), one looks at a distant point of light, he will 
see instead of a point a long, bright streak, red at one end and 
violet at the other. If the object looked at is a line of light, 
parallel to the edge of the prism or to the lines of the grating, 
then instead of a colored streak without width, he gets a 
colored band or ribbon of light, the spectrum, which may show 
markings which will give him much valuable information. It 
is usual to form this line of light by admitting the rays 
through a narrow " slit " placed at one end of a tube, which 
carries at the other end an achromatic object-glass having 
the slit in the principal focus. This tube, with slit and lens, 
constitutes the " collimator. 7 ' Instead of looking at the spec- 
trum with the naked eye, it is better also in most cases to use 
a small "view telescope," so called to distinguish it from the 
large telescope to which the spectroscope is often attached. 

1 The " grating " is merely a piece of glass or speculum metal, ruled with 
many thousand straight, equidistant lines, from 5000 to 20,000 in the 
inch. 



§ 172] 



THE SPECTROSCOPE. 



125 



172. Construction of the Spectroscope. — The instrument, 
therefore, as usually constructed, and shown in Fig. 32, con- 
sists of three parts, — collimator, dispersion-piece, and view 



Prism-Spectroscope 




F%k 1 


1 ' — 


■Ntr.1 


1 


f 1 ^M^ 


Collimator 




Grating-Spectroscope 
Collimator ,S 2 



Grating 



Direct-Vision Spectroscope 
Fig. 32. — Different Forms of Spectroscope. 

telescope, — although in the " direct-vision " spectroscope, 
shown in the figure, the view telescope is omitted. If the slit 
S be illuminated by strictly homogeneous light (i.e., light all 
of one color), say yellow, the "real image " of the slit will be 
found at T. If, at the same time, light of a different color 
— red for instance — be also admitted, a second image will be 
formed at R, and the observer will then see a spectrum with 
two bright lines, the lines being really nothing more than images 
of the slit. 

If violet light be admitted, a third image will be formed at 
V, and there will be three bright lines. If light from a candle 
be admitted, there will be an infinite number of these slit- 
images close together, like the pickets in a fence, without 
interval or break, and we then ge* what is called a ' continu- 



126 THE SPECTROSCOPE. [§ 172 

ous ' spectrum. If, however, we look at sunlight or moonlight 
or- the light of a star, we shall find a spectrum continuous in 
the main, but crossed by numerous dark lines, or missing slit- 
images (as if some of the fence-pickets had been knocked off, 
leaving gaps). 

173. Principles upon which Spectrum Analysis depends. — 

These, substantially, as announced by Kirchhoff in 1858, are 
the three following : — 

1st. A continuous spectrum is given by bodies which are so 
dense that the molecules interfere with each other in such a 
way as to prevent their free vibration ; i.e., by bodies which 
are either solid or liquid, or, if gaseous, are under pressure. 

2d. The spectrum of a luminous gas under low pressure is 
discontinuous, that is, it is made up of bright lines or bands, and 
these lines are characteristic. The same substance under simi- 
lar cojiditions always gives the same set of lines, and usually 
it does so even under conditions which differ rather widely ; 
but when the circumstances differ too much, it may give two 
or more different spectra. 

3d (and most important for our purpose just now). A gas or 
vapor absorbs from a beam of white light passing through it 
precisely those rays of which its own spectrum consists; so that 
the spectrum of white light which has been transmitted 
through such a vapor, if the vapor is cooler than the original 
source of light, exhibits a " reversed " spectrum of the gas ; 
i.e., we get a spectrum which shows dark lines in place of the 
characteristic bright lines. 

We therefore infer that the sun is covered by an envelope . 
of gases, not so hot as the luminous clouds which form the 
photosphere, and that these gases by their absorption produce 
the dark lines which we see. 



§174] 



SPECTRUM ANALYSIS. 



127 



174. Experiment illustrating Reversal of Spectrum. — The 

principle of reversal is illustrated by Fig. 33. Suppose that 
in front of the spectroscope we place a spirit lamp with a little 



Screen, 




Fig. 33. — Reversal of the Spectrum. 

carbonate of soda and some salt of thallium upon the wick. 
We shall then get a spectrum showing the two yellow lines of 
sodium and the green line of thallium, all bright, as in the 
upper of the two spectra. If now the lime light be started 
behind the flame, we shall at once get the effect shown in the 
lower figure, — a continuous spectrum crossed by three black 
lines which exactly replace the bright ones. Thrust a screen 
between the lamp flame and the lime, and the dark lines 
instantly turn bright again. 

The dark lines which appear when the screen is removed are dark 
only relatively to the background : when the screen is taken away they 
really brighten a little (say 2 or 3 per cent) ; but the brightness of the 
background increases hundreds of times, and so far exceeds that of 
the lines themselves that they look black. 



128 



ELEMENTS IN THE SUN. 



[§175 



175. Chemical Constituents of the Solar Atmosphere. — By 

taking advantage of these principles, we can detect a large 
number of well-known terrestrial elements in the sun. The 
solar spectrum is crossed by dark lines/ which with an instru- 
ment of high power number several thousand. 

By proper arrangements it is possible to identify among 
these lines many which are due to the presence in the sun's 
atmosphere of known terrestrial elements in the state of 
vapor. To effect the comparison necessary for this purpose, 
the spectroscope must be so arranged that the observer can 
confront the spectrum of sunlight with that of the substance 
to be tested. In order to do this, half of the slit is covered 
by a little reflector or "comparison prism," which reflects into 
the tube the light of the sun, while the other half of the 
slit receives directly the light of some flame or electric 
spark. On looking into the spectroscope, the observer will 
then see a spectrum, the lower half of which, for instance, is 




Fig. 34. — Comparison of the Spectrum of Iron with the Solar Spectrum. From a 
Negative by Professor Trowbridge. 

made by sunlight, while the upper half is made by light com- 
ing from an electric spark between two metal points, say of 
iron. This latter spectrum will show the bright lines of iron 
vapor, and the observer can then easily see whether they do 
or do not correspond exactly with the dark lines of the solar 
spectrum. 



1 They are generally referred to as Fraunhofer's lines, because Fraun- 
hofer was the first to map them. To some of the principal ones he 
assigned letters of the alphabet, which are still retained ; thus A is a 
strong red line at the extreme end of the spectrum ; C, one in the scarlet ; 
D, one in the yellow ; and H, one in the violet. 



§175] 



ELEMENTS IN THE SUN. 



129 



In such comparisons photography may be most effectively used 
instead of the eye. Fig. 34 is a rather unsatisfactory reproduction, 
on a reduced scale, of a negative made by Professor Trowbridge of 
Cambridge. The lower half is the violet portion of the sun's spec- 
trum, and the upper half that of an electric arc charged with the 
vapor of iron. 1 The reader can see for himself with what absolute 
certainty such a photograph indicates the presence of iron in the solar 
atmosphere. A few of the lines in the photograph which do not show 
corresponding lines in the solar spectrum are due to impurities in the 
carbons of the electric arc, and not to iron. 

176. Elements known to exist in the Sun. — As the result of 
such, comparisons, we have the following list of thirty-six 
elements which are now (1895) known to exist in the sun : — 



* Calcium, 11. 

* Iron, 1. 

* Hydrogen, 22. 

* Sodium, 20. 

* Nickel, 2. 

* Magnesium, 19. 

* Cobalt, 6. 
Silicon, 21. 
Aluminium, 25. 

* Titanium, 3. 

* Chromium, 5. 

* Manganese, 4. 



* Strontium, 23. 
Vanadium, 8. 

# Barium, 24. 
Carbon, 7. 
Scandium, 12. 
Yttrium, 15. 
Zirconium, 9. 
Molybdenum, 11 
Lanthanum, 14. 
Niobium, 16. 
Palladium, 18. 



Copper, 30. 
Zinc, 29. 
Cadmium, 26. 

# Cerium, 10. 
G-lucinum, 33. 
Germanium, 32. 
Rhodium, 27. 
Silver, 31. 
Tin, 34. 

Lead. 35. 
Erbium, 28. 

• Potassium, 36. 



Neodymium, 13. 

The substances are arranged according to the intensity of the dark 
lines by which they are represented in the solar spectrum, while the 
numbers appended indicate the rank which each would hold if the 
arrangement had been based upon the number of lines. An asterisk 
denotes that the lines of the element often or always appear as bright 
lines in the spectrum of the chromosphere. (Art. 180.)' 

In the atmosphere of the sun these bodies must be, of course, 
in the condition of vapor, which is somewhat cooler than 

1 Of course, in the negative, dark lines show bright, and vice versa. 



130 THE REVERSING LAYER. [§ 176 

the clouds which form the photosphere. It will be noticed 
that all of them, carbon alone excepted, are metals (chemically 
hydrogen is as much a metal as any of the others), and that a 
number of the elements which are among the most important 
in the constitution of the earth fail to present themselves. 
Thus far oxygen, nitrogen, chlorine, bromine, iodine, sulphur, 
phosphorus, and mercury all appear to be missing. 

We must be cautious, however, in drawing negative con- 
clusions. It is quite possible that the spectra of these bodies 
under solar conditions may be so different from their spectra 
as presented in our laboratories, that we cannot easily recog- 
nize them : many substances, under different conditions, give 
two or more widely different spectra. 

177. The Reversing Layer. — According to Kirchhoff's theory 
the dark lines are formed by the passing of light emitted by 
minute solid or liquid particles of photospheric clouds through 
the somewhat cooler vapors which compose the substances 
that we recognize by the dark lines in the spectrum. If this 
is so, the spectrum of the gaseous envelope, which by its 
absorption forms the dark lines, ought to show a spectrum of 
corresponding bright lines when seen by itself. The oppor- 
tunities are rare when it is possible to obtain a spectrum of 
this gaseous envelope separate from that of the photosphere ; 
but at the time of a total eclipse, at the moment when the 
sun's disc has just been obscured by the moon, and the sun's 
atmosphere is still visible beyond the moon's limb, the ob- 
server ought to see this bright-line spectrum, if the slit of the 
spectroscope be carefully directed to the proper point ; and the 
observation has actually been made. The lines of the solar 
spectrum, which up to the time of the total obscuration of the 
sun remain dark as usual, are suddenly reversed, and the whole 
field of the spectroscope is filled with brilliant colored lines, 
which flash out quickly, and then gradually fade away, disap- 
pearing in about two seconds. 



§177] 



SUN-SPOT SPECTRUM. 



131 



The natural interpretation of this phenomenon is that the 
formation of the dark lines in the solar spectrum is, mainly at 
least, produced by a very thin stratum closely covering the 
photosphere, since the moon's motion in two seconds would 
correspond to a thickness of only 500 miles. 

There are reasons, however, to doubt whether the lines are all 
produced in such a thin layer. According to Mr. Lockyer, the solar 
atmosphere is very extensive, and certain lines of the spectrum appear 
to be formed only in the regions of lower temperature high up above 
the surface of the photosphere. It is probable also that many lines 
originate within the photosphere and not above it, being caused by 
the vapors which lie between the cloud-masses that give the brilliant 
light. 



178. Sun-Spot Spectrum. — The spectrum of a sun spot 
differs from the general solar spectrum not only in its dimin- 
ished brilliancy, but in the great widening of certain lines, the 
thinning of others, and the change of some (especially the lines 
of hydrogen) to bright lines on some occasions. The majority 
of the Fraunhofer lines, however, are not much affected either 
way. 

In the green and blue portions of the spectrum the darkest 
part of a sun-spot spectrum is found to be composed of fine 
dark lines close packed. This shows that the darkening is 
due to the absorption of light by gases and vapors ; not by 
mist or smoke, for then the spectrum would be continuous. 

Sometimes, in connection with sun spots, certain lines of the 
spectrum are bent and broken, as shown in Fig. 35. These 

distortions are explained by 
the swift motion towards or 
from the observer of the 
gaseous matter, which by 
its absorption produces the 
line in question. In the case 
illustrated in the figure, hy- 
drogen was the substance. 



j 



i 



2 h 43 m 2 h 46 m 2*» 51 m 

Fig. 35. — The C line in the Spectrum of a 

Sun Spot. 



132 THE CHROMOSPHERE. [§ 178 

and its motion was towards the observer, nearly at the rate of 
300 miles a second at one point. 

179. Doppler's Principle. — The principle npon which the 
explanation of this displacement and distortion of lines de- 
pends was first enunciated by Doppler in 1842. It is this: 
when the distance between us and a body ivhich is emitting regular 
vibrations, either of sound or of light, is decreasing, then the 
number of pulsations received by us in each second is increased, 
and the length of the waves is correspondingly diminished. Thus 
the pitch of a musical tone rises in the case supposed, and in 
the same way the refrangibility of a light wave, which depends 
upon its wave length, is increased, so that it will fall nearer 
the violet end of the spectrum. This principle finds numerous 
applications in modern astronomical spectroscopy, and* it is of 
extreme importance that the student should clearly under- 
stand it. 

180. The Chromosphere. — Outside the photosphere, or shin- 
ing surface of the sun, lies the so-called chromosphere, of which 
the stratum of gases that produce the dark lines in the solar 
spectrum is the hottest and densest portion. The word is 
derived from the Greek, chroma (color), and means "color- 
sphere." It is so-called because it is brilliantly scarlet, owing 
this color to the hydrogen gas which is its most conspicuous 
component. In structure, it is like a sea of flame, covering 
the photosphere to a depth of from 5000 to 10,000 miles, and 
as seen through a telescope at the time of a total eclipse, it 
has been well described as looking like a "prairie on fire." 
There is, however, no real burning in the case ; i.e., no heat- 
producing combination of hydrogen with oxygen, or with any 
other element. 

Under ordinary circumstances the chromosphere is invisible, 
drowned in the light of the photosphere. It can be seen with 
the telescope only for a few seconds at a time, during the fleet- 



§ 180] PROMINENCES AND CHROMOSPHERE. 133 

ing moments of a total eclipse ; but with the spectroscope it 
can be studied at other times, as we shall see. 

181. Prominences. — The prominences, or protuberances, are 
scarlet clouds which are seen during a total eclipse, projecting 
from behind the edge of the moon. They are simply exten- 
sions of the chromosphere, or isolated clouds of the same 
gaseous substances, chiefly hydrogen. Their true nature was 
established at an eclipse in 1868, when their spectrum was 
first satisfactorily made out. The spectrum is composed of 
numerous bright lines, conspicuous among which are the lines 
of hydrogen, together with a brilliant yellow line (sometimes 
called D 3 because near the two so-called D lines) and the so- 
called H and K lines of calcium, with a number of others 
that are always present though more difficult to observe. At 
times also when the solar forces are peculiarly energetic hun- 
dreds of other lines appear, especially those of iron, titanium, 
magnesium and sodium. For a long time the D s line remained 
entirely unidentified, and the name of helium, or "sun-metal," 
was proposed and accepted for the hypothetical element to 
which it is due. In 1895, however, Dr. Ramsay, one of the 
discoverers of " argon" found the D s line in the spectrum a 
gas disengaged by heating and pumping from a rare mineral 
known as uranirrite, and very soon it was found by him and 
other observers in various other minerals and in meteoric 
iron. Along with the D 3 line, were also found several other 
unidentified lines of the chromosphere spectrum, which, with 
D 3 and the hydrogen lines, are also found in the spectra of 
certain nebulae and variable stars. It was a great triumph 
thus to " run helium to earth," though as yet very little is 
known as to its nature and properties except that, next to 
hydrogen, it is the lightest of all known gases, and in 
chemical inertness appears to resemble argon itself. 

182. Spectroscopic Observations of the Prominences and Chro- 
mosphere. — Since the spectrum of these objects is composed 



134 PHOTOGRAPHY OF PROMINENCES. [§ 182 

of a small number of brilliant lines, it is possible to observe 
them with a spectroscope in full daylight. The explanation 
of the way in which the spectroscope effects this lies rather 
beyond our limitations ; but it is sufficient for our purpose to 
say that by attaching a spectroscope to a good telescope the 
prominences can now be studied at leisure any clear day. They 
are wonderfully interesting and beautiful objects. Some of 
them, the so-called " quiescent " prominences, are of enormous 
size, 50,000 or even 100,000 miles in height, faint and diffuse, 
remaining almost unchanged for days. Others are much more 
brilliant and active, especially those that are associated with 
sun spots, as many of them are. These "eruptive" promi- 
nences often alter their appearance very rapidly, — so fast 
that one can sometimes actually see the motion : velocities 
from 50 to 200 miles a second are frequently met with. As a 
rule the eruptive prominences are not so large as the quiescent 
ones, but occasionally they surpass them, and a few have been 
observed to attain elevations of more than 200,000 miles. 
Fig. 36 gives specimens of both kinds. 

182.* Photography of Prominences. — Quite recently it has 
become possible to photograph these objects at anytime by 
utilizing the H and K lines in their spectrum. An explana- 
tion of the method lies quite beyond our scope, but Professor 
Hale, the director of the new Yerkes Observatory, and Des- 
landres in Paris, have been specially successful in this line, 
and have both constructed spectroscopic apparatus with which, 
at a single operation, they obtain a picture of the entire chro- 
mosphere and its prominences, surrounding an image of the 
sun itself with its spots and faculous regions. The solar 
image is really only a picture of those parts of the disc where 
the calcium lines are bright, and is by no means so perfect a 
picture as photographs made in the usual way : but it is 
sufficient to show how the prominences stand related to the 
solar surface, and its comparison with an ordinary photo- 
graph brings out many interesting peculiarities. The new 
method is a great step in the study of solar physics. 



183] 



THE CORONA. 



135 



183. The Corona. — Probably the most beautiful and im- 
pressive of all natural phenomena is the corona, the " glory" 
of light which surrounds the sun at a total eclipse. The por- 





Quiescent Prominences. 




Flames. Jets and Spikes near Sun's Limb, Oct. 5, 1871. 

Eruptive Prominences. 
Fig. 36. 

tion of it near the sun is dazzlingly bright and of a pearly 
lustre, contrasting beautifully with the scarlet prominences, 
which stud it like rubies. It seems to be mainly composed 
of projecting filaments of light, which near the sun are 
pretty well defined, but at a little distance fade out and melt 
into the general radiance. Near the poles of the sun the 
corona does not usually extend very far and has a pretty 
definite outline, but in the spot regions and near the sun's 
equator faint streams sometimes extend to a distance of sev- 



136 



THE CORONA. 



[§ 183 



eral degrees ; and at the distance of the sun every degree 

means more than a million of miles. 

A very striking and perplexing feature is the existence of 

perfectly straight dark rays or rifts, which reach clear down 

to the very edge of the sun. 

The corona varies very greatly in brightness at different 

eclipses, according to the apparent diameter of the moon at 

the time. The portion of 
the corona nearest the sun 
is so much brighter than 
the outer regions that 
a little increase of the 
moon's diameter cuts off 
a very large proportion of 
the light. The total light 
of the corona is usually at 
least two or three times 
as great as that of the full 
moon. 

Fig. 37 represents the 
corona as seen in the 
eclipse of 1882. 

184. Spectrum of the 
Corona. — A characteris- 
tic feature of its spectrum 
is a bright green line, 
generally known as the 
"1474" line. 1 This line was at first -supposed to be due to 
iron, and the coincidence was for a long time puzzling (since 
the vapor of iron is a very improbable substance to be found 
at an elevation above the hydrogen of the chromosphere), until 

1 So-called because it coincides with a dark line on Kirchhoff's map of 
the solar spectrum, which was the chart in use when the line was first 
discovered, in 1869. 




Fig. 37. 
Corona of the Egyptian Eclipse, 1882. 



§ 184 ] THE CORONA. 137 

it was discovered that the line is really a close double. One of 
the two components of the dark line is due to iron, while the 
other, the true corona line, is due to some still unknown gaseous 
element (probably lighter than hydrogen), which has been 
called coronium, after the analogy of helium. It is to be 
hoped that before very long this substance also may be " run 
to earth " as helium has been. 

Besides this conspicuous green line, the hydrogen lines are 
also faintly visible in the corona spectrum ; and by means of 
photography it has been found that the violet and ultra-violet 
portions of the spectrum are also rich in bright lines, the two 
wide lines or bands, known as H and K in the ordinary solar 
spectrum, being especially bright and conspicuous. 

185. The corona is proved to be a true appendage of the 
sun, and not, as has been at times supposed, a mere optical 
phenomenon, nor one due to the atmosphere of the earth or 
moon, by two established facts : — 

1st. That its spectrum is not that of reflected sunlight, but 
of a self-luminous gas ; and 

2d. Because photographs of the corona, made at widely dif- 
ferent stations along the track of an eclipse, agree exactly in 
details. 

Its real nature and relation to the sun is very difficult to 
explain. It is a gaseous envelope, at least mainly gaseous, as 
our atmosphere is, but it does not stand in any such relations 
to the globe beneath as does the air. Its phenomena are not 
yet satisfactorily explained, and remind us far more of auroral 
streamers and of comets' tails than of anything that occurs in 
the lower regions of the earth's atmosphere. The material of 
the corona is of excessive rarity, as is shown by the fact that 
in a number of cases comets have passed directly through it 
(as, for instance, in 1882) without the slightest perceptible 
disturbance. Its density, therefore, must be almost incon- 
ceivably less than that of the best vacuum which we are able 
to produce. 



138 sun's light and heat. [§ 186 

SUN'S LIGHT AND HEAT. 

186. The Sun's Light. — By photometric measures, which 
we cannot explain here, it is found that the sun gives us 1575 
billions of billions (1575 followed by 24 ciphers) times as 
much light as a standard candle 1 would do at that distance. 

The amount of light received from the sun is about 600,000 
times that given by the full moon, about 7^00,000000 times 
that of Sirius, the brightest of the fixed stars, and fully 
200,000,000000 times that of the Pole-star. As to the inten- 
sity of sunlight, or the intrinsic brightness of the sun's sur- 
face, we find that it is about 190,000 times as bright as that 
of the candle flame, and fully 150 times as bright as the lime 
of a calcium light ; so that even the darkest part of a sun spot 
outshines the lime light. The brightest part of an electric arc- 
light comes nearer sunlight in intensity than anything else we 
know of, being from a half to a quarter as bright as the solar 
surface itself. 

The sun's disc is brightest near the centre, but the variation 
is slight until we get pretty near the edge, where the light 
falls off rapidly. Just at the sun's limb, the brightness is not 
much more than a third as great as at the centre. The color 
also is there modified, becoming a sort of an orange-red. This 
darkening and change of color are due to the general absorp- 
tion of light by the lower portions of the sun's atmosphere. 
According to Langley, if this atmosphere were suddenly re- 
moved the surface would shine out somewhere from two to 
five times as brightly as now, and its tint would become 
strongly blue, like the color of an electric arc. 

187. The Quantity of Solar Heat ; the Solar Constant. — The 

" solar constant " is the number of heat units which a square 
unit of the earth's surface, unprotected by any atmosphere and 

1 The standard candle is a sperm candle weighing one- sixth of a pound 
and burning 120 grains an hour. An ordinary gas-burner usually gives a 
light equivalent to from ten to fifteen candles. 



§ 187] THE SUN'S HEAT. 139 

squarely exposed to the sun's rays, would receive from the sun 
in a unit of time. The heat-unit most used at present is the 
" calory/' l which is the quantity of heat required to raise the 
temperature of one kilogram of water 1° C. ; and as the result 
of the best observations thus far made (Langley's) it appears 
that the "Solar Constant" is approximately thirty of these 
calories to a square metre in a minute. At the earth's surface 
a square metre, owing to the absorption of a large percentage 
of heat by the air, would, however, seldom actually receive 
more than from ten to fifteen calories in a minute. 

The method of determining the solar constant is simple, as 
far as the principle goes, but the practical difficulties are 
serious, and thus far have prevented our obtaining all the 
accuracy desirable. The determination is made by allowing a 
beam of sunlight of known diameter to fall upon a known 
quantity of water for a known time, and measuring how much 
the water rises in temperature. The principal difficulty lies 
in determining the proper allowance to be made for absorption 
of the sun's heat in passing through the air. Besides this it 
is necessary to measure, and allow for, the heat which is re- 
ceived by the water from other sources than the sun. 

188. Solar Heat at the Earth's Surface. — Since it requires 
about eighty calories of heat to melt one kilogram of ice, it 
follows that, taking the solar constant at thirty, the heat 
received from the sun when overhead would melt in an hour 
a sheet of ice about nine-tenths of an inch thick. From this 
it is easily computed that the amount of heat received by the 
earth from the sun in a year would melt a shell of ice 165 
feet thick all over the earth's surface. 

"Solar engines" have been constructed within the last few 
years, in which the heat received upon a large reflector is 
made to evaporate water in a suitable boiler and to drive a 

1 A " small calory M is also used, one thousandth as large as this : viz. 
the quantity of heat which will raise the temperature of one gram of 
water 1° C. 



140 RADIATION FROM THE SUn's SURFACE. [§ 188 

steam engine. It is found that the heat received upon a re- 
flector ten feet square can be made to give practically about 
one horse-power. 

189. Radiation from the Sun's Surface. — If we attempt to 
estimate the intensity of the radiation from the surface of the 
sun itself, we reach results which are simply amazing. We 
must multiply the solar constant observed at the earth by the 
square of the ratio between the earth's distance from the sun 
and the distance of the sun's surface from its own centre ; i.e., 

by the square of ( ~— ^ - ^ \ or about 46,000 : in other words, 
J ^ \ 433,250 / 

the amount of heat emitted in a minute by a square foot of 
the sun's surface is about 46,000 times as great as that received 
by a square foot of surface at the distance of the earth. Car- 
rying out the figures, we find that if the sun were frozen 
over completely to a depth of over sixty feet, the heat it emits 
would be sufficient to melt the ice in one minute ; that if a 
bridge of ice could be formed from the earth to the sun by an 
ice-column 2\ miles square, and if in some way the entire solar 
radiation could be concentrated upon it, it would be melted in 
one second, and in seven more would be dissipated in vapor. 

Expressing it in terms of energy, we find that the solar radi- 
ation is more than 120,000 horse-power continuously, for each 
square metre of the sun's surface. 

So far as we can now see, only a very small fraction of this whole 
radiation ever reaches a resting-place. The earth intercepts about 
STcnrrTnnRTtf an( * the other planets of the solar system receive in all 
perhaps from ten to twenty times as much. Something like TSTruirafun 
seems to be utilized within the limits of the solar system. 

190. The Sun's Temperature. — We can determine with some 
accuracy the amount of heat which the sun gives ; to find its 
temperature is a very different thing, and we really have very 
little knowledge about it, except that it must be extremely 



§ 190] CONSTANCY OF THE SUN'S HEAT. 141 

high, — far higher than that of any terrestrial source of heat 
now known. The difficulty is that our laboratory experiments 
do not give the necessary data from which we can determine 
what temperature substances like those of which the sun is 
composed must have, in order to enable them to send out 
heat at the rate which we observe. Of two bodies at precisely 
the same temperature, one may send out heat a hundred times 
more rapidly than the other. 

The estimates as to the temperature of the photosphere run 
all the way from the very low ones of some of the French 
physicists (who set it at about 2500° C.) to those of Secchi 
and Ericsson, who put the figure among the millions. The 
prevailing opinion sets it between 5000° and 10,000° C, or 
from 9000° to 18,000° F. 1 

A very impressive demonstration of the intensity of the 
sun's heat is found in the fact that in the focus of a powerful 
burning lens all known substances melt and vaporize ; and yet 
it can be shown that at the focus of the lens the temperature 
can never even nearly equal that of the source from which the 
heat is derived. 

191. Constancy of the Sun's Heat. — It is still a question 
whether the total amount of the sun's radiation does or does 
not vary from time to time. There may be considerable fluc- 
tuations in the hourly or daily quantity of heat, without our 
being able to detect them with our present means of observation. 

As to any steady progressive increase or decrease in the 
amount of heat received from the sun, it is quite certain that 
no considerable change has occurred for the past 2000 years, 
because the distribution of plants and animals on the earth's 
surface is practically the same as in the earliest days of his- 
tory. It is, however, rather probable than otherwise that the 
great changes of climate, which Geology indicates as having 
formerly taken place on the earth, may ultimately be traced 
to changes in the condition of the sun. 

1 The determination of Wilson and Gray in 1893-5, makes it 8000° C, 
pr a little more than 14,000° F. 



142 MAINTENANCE OF THE SOLAR HEAT. [§ 192 

192. Maintenance of the Solar Heat. — We cannot here dis- 
cuss the subject fully, but must content ourselves with saying, 
first, negatively, that this maintenance cannot be accounted 
for on the supposition that the sun is a hot body, solid or 
liquid, simply cooling ; nor by combustion ; nor (adequately) 
by the fall of meteors on the sun's surface, though this cause 
undoubtedly operates to a limited extent. Second, we can say 
positively that the solar radiation can be accounted for on the 
hypothesis first proposed by Helmholtz, that the sun is mainly 
gaseous, and shrinking slowly but continuously. While we 
cannot see any such shrinkage, because it is too slow, it is a 
matter of demonstration that if the sun's diameter should con- 
tract about 300 feet a year, heat enough would be generated 
to keep up its radiation without any lowering of its tem- 
perature. If the shrinkage were more than about 300 feet, 
the sun would be hotter at the end of the year than it was at 
the beginning. 

We can only say that while no other theory meets the con- 
ditions of the problem, this appears to do so perfectly, and 
therefore has probability in its favor. 

193. Age and Duration of the Sun. — Of course if this 
theory is correct, the sun's heat must ultimately come to an 
end ; and looking backward it must have had a beginning. If 
the sun keeps up its present rate of radiation, it must, on this 
hypothesis, shrink to about half its diameter in some 5,000000 
years at the longest. It will then be eight times as dense as 
now, and can hardly continue to be mainly gaseous, so that 
the temperature must begin to fall quite sensibly. It is not, 
therefore, likely, in the opinion of Professor Newcomb, that 
the sun will continue to give heat sufficient to support the 
present conditions upon the earth for much more than 
10,000000 years, if so long. 

On the other hand, it is certain that the shrinkage of the 
sun to its present dimensions from a diameter larger than that 



§ 193] CONSTITUTION OF THE SUN. 143 

of the orbit of Neptune, the remotest of the planets, would 
produce about 18,000000 times as much heat as the sun now 
throws out in a year; hence, if the sun's heat has been, and 
still is, wholly due to the contraction of its mass, it cannot have 
been emitting heat at the present rate, on this shrinkage hy- 
pothesis, for more than 18,000000 years. But notice the 'if. 7 
It is quite possible that the solar system may have received 
in the past supplies of heat other than that due to the con- 
traction of the sun's mass. If so, it may be much older. 

194. Constitution of the Sun. — To sum up : The received 
opinion as to the constitution of the sun is that the central 
mass, or nucleus, is probably gaseous, under enormous pressure, 
and at an enormous temperature. 

The photosphere is probably a sheet of luminous clouds, con- 
stituted mechanically like terrestrial clouds, that is, of small, 
solid, or liquid particles, very likely of carbon, floating in gas. 

These photospheric clouds float in an atmosphere composed 
of those gases which do not condense into solid or liquid par- 
ticles at the temperature of the solar surface. This atmos- 
phere is laden, of course, with the vapors out of which the 
clouds have been condensed, and constitutes the reversing layer 
which produces the dark lines of the solar spectrum. 

The chromosphere and prominences appear to be composed of 
permanent gases, mainly hydrogen and helium, which are min- 
gled with the vapors in the region of the photosphere, but rise 
to far greater elevations. For the most part the prominences 
appear to be formed by jets of hydrogen, ascending through 
the interstices between the photospheric clouds, like flames 
playing over a coal fire. 

As to the corona, it is as yet impossible to give any satis- 
factory explanation of all the phenomena that it presents, and 
since thus far it has been possible to observe it only during 
the brief moments of total eclipses, progress in its study has 
been necessarily slow. 



144 ECLIPSES. [ § 195 



CHAPTER VII. 

ECLIPSES AND THE TIDES. — FORM AND DIMENSIONS OF 
SHADOWS. — ECLIPSES OF THE MOON. — SOLAR ECLIPSES, 
— TOTAL, ANNULAR, AND PARTIAL. — NUMBER OF 
ECLIPSES IN A YEAR.- — RECURRENCE OF ECLIPSES 
AND THE SAROS. — OCCULTATIONS. — THE TIDES. 

195. The word Eclipse (literally a ( swoon') is a term ap- 
plied to the sudden darkening of a heavenly body, especially 
of the sun or moon. An eclipse of the moon is caused by its 
passing through the shadow of the earth; an eclipse of the 
sun by the moon's passing between the sun and the observer, 
or, what comes to the same thing, by the passage of the 
moon's shadow over the observer. The ( Shadow,' in Astron- 
omy, is the space from which sunlight is excluded by an inter- 
vening body : speaking geometrically, it is a solid, not a surface. 
If we regard the sun and the other heavenly bodies as spheri- 
cal, which, of course, they are very nearly, these shadows are 
cones with their axes in the line which joins the centres of the 
sun and the shadow-casting body, the point being always 
directed away from the sun. If interplanetary space were a 
little hazy, we should see every planet accompanied by its 
shadow, like a black tail behind it. 

ECLIPSES OF THE MOON. 

196. Dimensions of the Earth's Shadow. — The length of 
the shadow is easily found. In Fig. 38, is the centre of the 
sun and E the centre of the earth, and Q>Cb is the shadow of 



196] 



THE} earth's SHADOW. 



145 



the earth cast by the sun. It is readily shown by Geometry 
that if we call EC, the length of the shadow, L, and OE, the 
distance of the earth from the sun, D, then 

L = D x | ^- \ R being OA the radius of the sun, and r 

I ), is about 

\lt - rf 



Jt - r 
the radius of the earth Ea. This fraction, 



— 1 — , so that L = — - Z>. 
108.5 108.5 

This gives 857,000 miles for the average length of the earth's 
shadow. The length varies about 14,000 miles on each side 




Fig. 38. — The Earth's Shadow. 

of the mean, in consequence of the variation of the earth's dis- 
tance from the sun at different times of the year. 

From the cone aCb all sunlight is excluded, or would be were it not 
for the fact that the atmosphere of the earth bends some of the rays 
which pass near the earth's surface into its shadow. The effect of 
this atmospheric refraction is to increase the diameter of the shadow 
about two per cent, but to make it less perfectly dark. 

If we draw the lines, Be and Ad, crossing at P, between the 
earth and the sun, thpy will bound the penumbra, within 
which a part, but not the whole, of the sunlight is cut off: an 
observer outside of the shadow, but within this partly shaded 
space, would see the earth as a black body encroaching on the 
sun's disc, but not covering it. 



146 LUNAR ECLIPSES. [§ 197 

197. Lunar Eclipses. — The axis, or central line, of the 
earth's shadow is always directed to a point directly opposite 
the sun. If, then, at the time of full moon the moon happens 
to be near the ecliptic, i.e., not far from one of the nodes (the 
points where her orbit cuts the ecliptic), she will pass through 
the shadow and be eclipsed. Since, however, the moon's orbit 
is inclined 5° 8' to the ecliptic, lunar eclipses do not happen 
very frequently, seldom more than twice a year ; because the 
moon at the full usually passes north or south of the shadow, 
without touching it. 

Lunar eclipses are of two kinds, partial and total; total 
when she passes completely into the shadow; partial when 
she only partly enters it, going so far to the north or south of 
the ceutre that only a portion of the disc is obscured. An 
eclipse of the moon when central (i.e., when the moon crosses 
the centre of the shadow) may continue total for about two 
hours, the interval from the first to the last contact being 
about two hours more. This depends upon the facts that the 
moon's hourly motion is nearly equal to its own diameter, and 
that the diameter of the earth's shadow where the moon 
crosses it is between two and three times the diameter of the 
moon itself. The duration of an eclipse that is not central varies 
of course with the part of the shadow traversed by the moon. 

198. Phenomena of Total Eclipses of the Moon. — Half an 
hour or so before the moon reaches the shadow, its edge begins 
to be sensibly darkened by the penumbra, and the edge of the 
shadow itself, when it first touches the moon, appears nearly 
black by contrast with the bright parts of the moon's surface. 
To the naked eye the outline of the shadow looks fairly sharp, 
but even with a small telescope it appears indefinite, and with 
a large telescope of high magnifying power the edge of the 
shadow becomes entirely indistinguishable, so that it is impos- 
sible to determine within half a minute or so the time when 
it reaches any particular point. 




§198] COMPUTATION OF A LUNAR ECLIPSE. 147 

After the moon has wholly entered the shadow, her disc is 
usually distinctly visible, illuminated with a dull copper- 
colored light, which is sunlight deflected around the earth into 
the shadow by the refraction of our atmosphere, as illustrated 
by Fig. 39. The brightness of the moon's disc during a total 
eclipse of the moon differs greatly at different times, according 



Up 

Fig. 39. — Light bent into Earth's Shadow by Refraction. 

to the condition of the weather on the parts of the earth which 
happen to lie at the edges of the earth's disc as seen from the 
moon. If it is cloudy and stormy there, little light will reach 
the moon ; if it happens to be clear, the quantity of light 
deflected into the shadow may be very considerable. In the 
lunar eclipse of 1884, the moon was for a time absolutely 
invisible to the naked eye, a very unusual circumstance. 

During the eclipse of Jan. 28th, 1888, although the moon was 
pretty bright to the eye, Pickering found that its photographic power, 
when centrally eclipsed, was only about ttoV o oo °f what it had been 
before the shadow covered it. 

199. Computation of a Lunar Eclipse. — The computation of 
a lunar eclipse is not at all complicated, though we do not propose to 
enter into it. Since all its phases are seen everywhere at the same 
absolute instant wherever the moon is above the horizon, it follows 
that a single calculation giving the Greenwich times of the different 
phenomena is all that is needed. Such computations are made and 
published in the Nautical Almanac. The observer needs only to cor- 
rect the predicted time by simply adding or subtracting his longitude 
from Greenwich, in order to get the true local time. With an eclipse 
of the sun the case is very different. 



148 



ECLIPSES OF THE SUN. 



[§200 



ECLIPSES OF THE SUN. 

200. The Length of the Moon's Shadow is very nearly 
3 ^ of its distance from the sun, and averages 232,150 miles. 
It varies not quite 4000 miles, ranging from 236,050 to 
238,300. 

Since the mean length of the shadow is less than the mean 
distance from the earth (238,800 miles), it is evident that on 
the average the shadow will fall short of the earth. The eccen- 
tricity of the moon's orbit, however, is so great that she is 
sometimes more than 30,000 miles nearer than at others. If 
when the moon is nearest the earth, the shadow happens to 
have at the same time its greatest possible length, its point 
may reach nearly 18,400 miles beyond the earth's surface. In 




To Sun 



Fig. 40. — The Moon's Shadow on the Earth. 

this CLse the "cross-section" of the shadow, where the earth's 
surface cuts it (at o in Fig. 40) will be about 168 miles in 
diameter, which is the largest value possible. On the other 
hand, when the moon is farthest from the earth, we may have 
the state of things indicated by placing the earth at B, in Fig. 
40. The vertex, V, of the shadow will then fall 24,700 miles 
short of the earth's surface, and the cross-section of the 
" shadow produced " will have a diameter of 206 miles at o\ 
where the earth's surface cuts it. 



201. Total and Annular Eclipses. — To an observer within 
the shadow-cone (i.e., between V and the moon, Fig. 40), the 
sun will be totally eclipsed. An observer in the " produced " 
cone, beyond V, will see the moon apparently smaller than the 



§201] PARTIAL ECLIPSES. 149 

sun, leaving a ring of the sun uneclipsed ; this is vvhat is 
called an " annular " eclipse. These annular eclipses are con- 
siderably more frequent than the total, and now and then an 
eclipse is annular in part of its course across the earth, and 
total in part. This is when the point of the moon's shadow 
extends beyond the surface of the earth, but does not reach as 
far as its centre. 

The track of the eclipse across the earth will of course be a 
narrow stripe having its width equal to the cross-section of 
the shadow, and extending across the hemisphere which is 
turned towards the moon at the time, though not necessarily 
passing the centre of that hemisphere. Its course is always 
from the west towards the east, but usually with considerable 
motion toward the north or south. 

202. The Penumbra and Partial Eclipses. — The penumbra 
can easily be shown to have a diameter on the line CD (Fig. 
40) a little more than twice the diameter of the moon, or over 
4000 miles. An observer situated within this penumbra has a 
partial eclipse. If he is near to the cone of the shadow, the 
sun will be mostly covered by the moon ; if near the outer 
edge of the penumbra, the moon will but slightly encroach on 
the sun's disc. While, therefore, a total or annular eclipse is 
visible as such only by observers within the narrow path trav- 
ersed by the shadow-spot, the same eclipse will be visible as a 
partial one anywhere within 2000 miles on each side of the 
path ; and the 2000 miles must be reckoned square to the axis 
of the shadow, and may correspond to a much greater distance 
when reckoned around upon the spherical surface of the earth. 

203. Velocity of the Shadow, and Duration of an Eclipse. 

— Were it not for the earth's rotation, the moon's shadow 
would pass the observer at the rate of about 2100 miles an 
hour. The earth, however, is rotating towards the east in the 
same general direction as that in which the shadow moves, 
so that the relative velocity is usually much less. 



150 PHENOMENA OF A SOLAR ECLIPSE. [§203 

A total eclipse of the sun observed at a station near the 
equator, under the most favorable conditions possible, may 
continue total for 7 m 58 s . In latitude 40° the duration can 
barely equal 6\ m . At the equator an annular eclipse may 
last for 12 m 24 s , the maximum width of the ring of the sun 
visible around the moon being V 37". 

In the observation of an eclipse, four contacts are recognized : the 
first, when the edge of the moon first touches the edge of the sun ; the 
second, when the eclipse becomes total or annular ; the third, at the ces- 
sation of the total or annular phase ; and the fourth, when the moon 
finally leaves the solar disc. From the first contact to the fourth the 
time may be a little over two hours. In a partial eclipse, only the 
first and fourth are observable, and the interval between them may be 
very small when the moon just grazes the edge of the sun. 

The magnitude of an eclipse is usually reckoned in " digits," the 
digit being -^ °f ^ ne sun's diameter. An eclipse of nine digits is 
one in which the disc of the moon covers three-fourths of the sun's 
diameter at the middle of the eclipse. 

204. Phenomena of a Solar Eclipse. — There is nothing of 
special interest until the sun is mostly covered, though before 
that time the shadows cast by the foliage begin to be peculiar. 

The light shining through every small interstice among the leaves, 
instead of forming as usual a circle on the ground, makes a little cres- 
cent — an image of the partly covered sun. 

About ten minutes before totality the darkness begins to be 
felt, and the remaining light, coming as it does from the edge 
of the sun, is not only faint but yellowish, more like that of a 
calcium light than sunshine. Animals are perplexed and 
birds go to roost. The temperature falls, and dew appears. 
In a few moments, if the observer is so situated that his view 
commands the distant western horizon, the moon's shadow is 
seen coming, much like a heavy thunder shower, and advanc- 
ing with almost terrifying swiftness. As soon as the shadow 
arrives, and sometimes a little before, the corona and promi- 



§204] CALCULATION OF A SOLAR ECLIPSE. 151 

. nences become visible, while the brighter planets and stars of 
the first three magnitudes make their appearance. 

The suddenness with which the darkness pounces upon the 
observer is startling. The sun is so brilliant that even the 
small portion which remains visible up to the moment of 
total obscuration so dazzles the eye that it is unprepared for 
the sudden transition. In a few moments, however, the eye 
adjusts itself, and it is found that the darkness is really not 
very intense. If the totality is of short duration, say not 
more than two minutes, there is not much difficulty in reading 
an ordinary watch-face. In an eclipse of long duration (four 
or five minutes) it is much darker, and lanterns become 
necessary. 

205. Calculation of a Solar Eclipse. — A solar eclipse cannot 
be dealt with in any such summary way as a lunar eclipse, because 
the times of contact and the phenomena are different at every differ- 
ent station. The path which the shadow of a total eclipse will 
describe upon the earth is roughly mapped out in the Nautical Alma- 
nacs several years beforehand, and with the chart are published the 
data necessary to enable one to calculate with accuracy the phenomena 
for any given station ; but the computation is rather long and some- 
what complicated. 

Oppolzer, a Viennese astronomer, published a few years ago a 
remarkable book entitled " The Canon of Eclipses," containing the 
elements of all eclipses (8000 solar and 5200 lunar) occurring between 
the year 1207 B.C. and 2162 a.d., with maps showing the approximate 
tracks of all the solar eclipses. 

206. Frequency of Eclipses and Number in a Year. — The 

least possible number in a year is two, both of the sun ; the 
largest seven, five solar and two lunar : the most usual number 
is four. The eclipses of a given year always take place at two 
opposite seasons, which maybe called the " eclipse months" 
of the year, near the times when the sun crosses the nodes of 
the moon's orbit. Since the nodes move westward around the 
ecliptic once in about nineteen years (Art. 134), the time oc- 



152 RECURRENCE OF ECLIPSES. [§ 206 

cupied by the sun in passing from a node to the same node 
again is only 346.62 days, which is sometimes called the 
"eclipse year." 

Taking the whole earth into account, the solar eclipses are 
the more numerous, nearly in the ratio of 3:2. It is not so, 
however, with those that are visible at a given place. A solar 
eclipse can be seen only by persons who happen to be on the 
track described by the moon's shadow in its passage across 
the globe, while a lunar eclipse is visible over considerably 
more than half the earth, either at its beginning or end, 
if not throughout its whole duration, — and this more than 
reverses the proportion; i.e., at any given place lunar eclipses 
are considerably more frequent than solar. Solar eclipses that 
are total somewhere or other on the earth's surface are not 
very rare, averaging about one for every year and a half. But 
at any given place a total eclipse happens only once in about 
360 years in the long run. 

During the 19th century, six shadow-tracks have already traversed 
the United States, and one more will do so on May 27th, 1900, the 
path in this case running from Texas to Virginia. 

207. Recurrence of Eclipses ; the Saros. — It was known to 
the Egyptians, even in prehistoric times, that eclipses occur 
at regular intervals of 18 years and 11^ days (10^ days if there 
happen to be five leap years in the interval). They named 
this period the " Saros." It consists of 223 synodic months, 
containing 6585.32 days, while 19 " eclipse years" contain 
6585.78. The difference is only about 11 hours, in which time 
the sun moves on the ecliptic about 28'. If, therefore, a solar 
eclipse should occur to-day with the sun exactly at one of the 
moon's nodes, at the end of 223 months the new moon will 
find the sun again close to the node (only 28' west of it), and 
a very similar eclipse will occur again ; but the track of this 
new eclipse will lie about 8 hours of longitude farther icest on 
the earth, on account of the odd .32 of a day in the Saros, 



§207] CAUSE OF THE TIDES. 153 

The usual number of eclipses in a Saros is a little over 70, 
varying two or three one way or the other. 

In the Saros closing Dec. 22d, 1889, the total number was 72, — 29 
lunar and 43 solar. Of the latter, 29 were central (13 total, 16 annu- 
lar), and 14 were only partial. 



THE TIDES. 

208. Cause of the Tides. — Since the tides depend upon the 
action of the sun and of the moon upon the waters of the 
earth, they may properly be considered here before we deal 
with the planetary system. We do not propose to go into the 
mathematical theory of the 
phenomena at all, as it lies 
far beyond our limitations ; 
but any person can see that 
a liquid globe falling freely 
towards an attracting body, 
which attracts the nearer por- 
tions more powerfully than 

r .,_ _ J _ Fig. 41. — The Tides. 

the more remote, will be drawn 

out into an elongated lemon-shaped form, as illustrated in 
Fig. 41 ; and if the globe, instead of being liquid, is mainly 
solid, but has large quantities of liquid on its surface, substan- 
tially the same result will follow. Now the earth is free in 
space, and though it has other motions, it is also falling towards 
the moon and towards the sun, and is affected precisely as it 
would be if its other motions did not exist. The consequence 
is that at any time there is a tendency to elongate those diam- 
eters of the earth which are pointed towards the moon and 
towards the sun. The sun is so much farther away than the 
moon that its effect in thus deforming the surface of the 
earth is only about two-fifths as great as that of the moon. 







154 DEFINITIONS. [§ 209 

209. The tides consist in a regular rise and fall of the ocean 
surface, the average interval between corresponding high 
waters on successive days at any given place being twenty- 
four hours and fifty-one minutes, which is precisely the same 
as the average interval between two successive passages of the 
moon across the meridian ; and since this coincidence is main- 
tained indefinitely, it of itself makes it certain that there must 
be some causal connection between the moon and the tides. 
Some one has said that the odd fifty-one minutes is the moon's 
" ear mark." 

That the moon is largely responsible for the tides is also 
shown by the fact that when the moon is in perigee, at the 
nearest point to the earth, the tides are nearly twenty per cent 
higher than when she is in apogee. 

210. Definitions. — While the water is rising, it is flood tide ; 
while falling, it is ebb tide. It is high water at the moment 
when the water level is highest, and low water when it is 
lowest. The spring tides are the largest tides of the month, 
which occur near the times of new and full moon, while the 
neap tides are the smallest, and occur at half moon, the rela- 
tive heights of spring and neap tides being about as 7 : 3. At 
the time of the spring tides, the interval between the corre- 
sponding tides of successive days is less than the average, 
being only about 24 hours, 38 minutes (instead of 24 hours, 
51 minutes), and then the tides are said to prime. At the neap 
tides, the interval is greater than the mean, — about 25 hours, 
6 minutes, and the tide lags. The establishment of a port is 
the mean interval between the time of high water at that port 
and the next preceding passage of the moon across the merid- 
ian. The " establishment "'of New York, for instance, is 8 
hours, 13 minutes. The actual interval between the moon's 
transit and high water varies, however, nearly half an hour 
on each side of this mean value at different times of the 
month, and under varying conditions of the weather. 



§211] MOTION OF THE TIDES. 155 

211. Motion of the Tides. — If the earth were wholly com- 
posed of water, and if it kept always the same face towards the 
moon, as the moon does towards the earth, then (leaving out 
of account the sun's action for the present) a permanent tide 
* would be raised upon the earth, as indicated in Fig. 41. The 
difference between the water level at A and D would be a 
little less than two feet. Suppose, now, the earth put in rota- 
tion. It is easy to see that the two tidal waves A and B would 
move over the earth's surface, following the moon at a certain 
angle dependent on the inertia of the water, and tending to 
move with a westward velocity equal to the earth's eastward 
rotation, — about a thousand miles an hour at the equator. 
The sun's action would produce similar tides superposed upon 
the moon's tide, and about two-fifths as large, and at different 
times of the month these two pairs of tides would sometimes 
conspire and sometimes be opposed. 

If the earth were entirely covered with deep water, the tide 
waves would run around the globe regularly ; and if the depth 
of the water were not less than thirteen miles, the tide crests, 
as can be shown (though we do not undertake it here), would 
follow the moon at an angle of just 90° : it would be high water 
just where it might at first be supposed we should get low 
water, the place of high water being shifted 90° by the rota- 
tion of the earth. 

If the depth of the water were, as it really is, much less 
than thirteen miles, the tide wave in the ofcean could not keep 
up with the moon, and this would complicate the results. 
Moreover, the continents of North and South America, with 
the southern Antarctic continent, make a barrier almost from 
pole to pole, leaving only a narrow passage at Cape Horn. As 
a consequence it is quite impossible to determine by theory 
what the course and character of tide waves must be. We 
have to depend upon observations, and observations are 
more or less inadequate, because, with the exception of a 
few islands, our only possible tide stations are on the shores 



156 FREE AND FORCED OSCILLATIONS. K 211 

of continents where local circumstances largely control the 
phenomena. 

212. Free and Forced Oscillations. — If the water of the 
ocean is suddenly disturbed, as, for instance, by an earth- n 
quake, and then left to itself, a " free wave " is formed, which, 
if the horizontal dimensions of the wave are large as compared 
with the depth of the water (i.e., if it is many hundred miles 
in length), will travel at a rate which depends simply on the 
depth of the water. 

Its velocity is equal, as can be proved, to the velocity acquired by a 
body in falling through half the depth of the ocean. Observations 
upon waves caused by certain earthquakes in South America and 
Japan have thus informed us that between the coasts of those coun- 
tries the Pacific averages between two and one-half and three miles in 
depth. 

Now as the moon in its apparent diurnal motion passes 
across the American continent each day and comes over the 
Pacific Ocean, it starts such a "parent" wave in the Pacific, 
and a second one is produced twelve hours later. These waves, 
once started, move on nearly (but not exactly) like a free earth- 
quake wave : not exactly, because the velocity of the earth's 
rotation being about 1040 miles at the equator, the moon 
moves (relatively) westward faster than the wave can natu- 
rally follow it ; and so for a while the moon slightly acceler- 
ates the wave. The tidal wave is thus, in its origin, a " forced 
oscillation " : in its subsequent travel it is very nearly, but 
not entirely, " free." 

Of course as the moon passes on over the Indian and Atlan- 
tic oceans, it starts waves in them also, which combine with 
the parent wave coming in from the Pacific. 

213. Course of Travel of the Tide Wave. — The parent wave 
appears to start twice a day in the Pacific Ocean, off Callao, on the 



§213] HEIGHT OF THE TIDES. 157 

coast of South America. From this point the wave travels northwest 
through the deep water of the Pacific, at the rate of about 850 miles an 
hour, reaching Kamtchatka in ten hours. Through the shallow water 
to the west and southwest the velocity is only from 400 to GOO miles an 
hour, so that the wave is six hours old when it reaches New Zealand. 
Passing on by Australia and combining with the small wave which the 
moon starts in the Indian Ocean, the resultant tide crest reaches the 
Cape of Good Hope in about twenty-nine hours, and enters the 
Atlantic. Here it combines with a smaller tide wave, twelve hours 
younger, which has " backed " into the Atlantic around Cape Horn, 
and it is also modified by the direct tide produced by the moon's 
action upon the Atlantic. The tide resulting from the combination of 
these three then travels northward through the Atlantic at the rate of 
about 700 miles an hour. It is about forty hours old when it first 
reaches the coast of the United States in Florida ; and our coast lies 
in such a direction that it arrives at all the principal ports within tw T o 
or three hours of the same time. It is forty-one or forty-two hours 
old when it reaches New York and Boston. To reach London, it has 
to travel around the northern end of Scotland and through the North 
Sea, and is nearly sixty hours old when it arrives at that port. 

In the great oceans there are three or four such tide crests, follow- 
ing nearly in the same track, but with continual minor changes. 

214. Height of the Tides. — In mid-ocean the difference 
between high and low water is usually between two and three 
feet, as observed on isolated islands in the deep water. On 
the continental shores the height is ordinarily much greater. 




Fig. 42. — Increase in Height of Tide on approaching the Shore. 

As soon as the tide wave "touches bottom/' so to speak, the 
velocity is diminished, the tide crests are crowded more closely 
together, and the height of the tide is very much increased, as 
indicated in Fig. 42. 



158 TIDES IN RIVERS. [§214 

Theoretically it varies inversely as the fourth root of the depth ; i.e., 
where the water is 100 feet deep, the tide wave should be twice as 
high as at the depth of 1600 feet. 

Where the configuration of the shore forces the tide into a 
corner, it sometimes rises very high. At Minas Basin on the 
Bay of Fundy, tides of seventy feet are not uncommon, and an 
altitude of 100 feet is said to occur sometimes. At Bristol 
in the English Channel, tides of forty or fifty feet are reached ; 
at the same time on the coast of Ireland, just opposite, the 
tide is very small. 

215. Tides in Rivers. — The tide wave ascends a river at a rate 
which depends upon the depth of the water, the amount of friction, 
and the swiftness of the stream. It may, and generally does, ascend 
until it comes to a rapid where the velocity of the current is greater 
than that of the wave. In shallow streams, however, it dies out 
earlier. Contrary to what is usually supposed, it often ascends to an 
elevation far above that of the highest crest of the tide wave at the 
river's mouth. In the La Plata and Amazon, the tide goes up to an 
elevation of at least 100 feet above the sea-level. The velocity of a 
tide wave in a river seldom exceeds ten or twenty miles an hour, and 
is ordinarily much less. 



§216] THE PLANETS IN GENERAL. 159 



CHAPTER VIII. 

THE PLANETARY SYSTEM. 

THE PLANETS IN GENERAL. — THEIR NUMBER, CLASSI- 
FICATION, AND ARRANGEMENT. — BODE's LAW. — THEIR 
^ ORBITS. — KEPLER'S LAWS AND GRAVITATION. — AP- 
PARENT MOTIONS AND THE SYSTEMS OF PTOLEMY 
AND COPERNICUS. DETERMINATION OF DATA RELAT- 
ING TO THE PLANETS, THEIR DIAMETER, MASS, ETC. — 
HERSCHEL'S ILLUSTRATION OF THE SOLAR SYSTEM. — 
DESCRIPTION OF THE TERRESTRIAL PLANETS, MERCURY, 
VENUS, AND MARS. 

216. The earth is one of a number of bodies called planets 
which revolve around the sun in oval orbits that are nearly 
circular and lie nearly in one plane or level. There are eight 
of them which are of considerable size, besides a group of sev- 
eral hundred minute bodies called the asteroids, which seem 
to represent in some way a ninth planet, either broken to 
pieces or somehow ruined in the making. 

217. Classification of the Planets. — The four inner ones 
have been called by Humboldt the terrestrial planets, because 
the earth is one of them, and the others resemble it in size 
and density. In the order of distance from the sun they are 
Mercury, Venus, the earth, and Mars. The four outer ones 
Humboldt calls the major planets, because they are much 
larger and move in larger orbits. They seem to be bodies of 
a different sort from the earth, very much less dense and 



160 



BODE S LAW. 



[§217 



probably of higher temperature, They are Jupiter, Saturn, 
Uranus, and Neptune. The asteroids (from the Greek aster- 
eidos, i.e., star-like planets), called by some planetoids, or 
minor planets, all lie in the vacant space between Mars and 
Jupiter, and appear to contain in the aggregate about as much 
material as would make a planet not far from the size of Mars. 
All of the planets except Mercury and Venus have satellites. 
The earth has one, Mars two, Jupiter four, Saturn eight, 
Uranus four, Neptune one, — twenty in all. 

218. The following little table contains in round numbers 
the principal numerical facts as to the planets : — 



Name. 


Distance in 

Astronomical 

Units. 


Period. 


Diameter. 


Mercury 

Venus 

Earth 

Mars 

Asteroids 

Jupiter 

Saturn 

Uranus 

Neptune ...... 


0.4 

0.7 

1.0 

1.5 

3.0 ± 

5.2 

9.5 
19.2 
30.1 


3 months 
7 J months 
1 year 

1 yr. 10 mos. 
3 years to 9 years 
11.9 years 
29.5 " 
84.0 " 
164.8 " 


3000 miles 

7700 " 

7918 » 

4200 " 
500 to 10 miles 
86,000 miles 
73,000 " 
32,000 " 
35,000 " 



This table should be learned by heart. More accurate data 
will be given hereafter, but the round numbers are quite suf- 
ficient for all ordinary purposes, and are much more easily 
remembered. 



219. Bode's Law. — If we set down a row of 4's, to the 
second 4 add 3, to the third 6, to the fourth 12, etc., a series of 
numbers will result which, divided by 10, will represent the 
planetary distances very nearly, except in the case of Neptune, 



§219] KEPLER'S LAWS. 161 

whose distance is only 30 instead of 38, as the rule would 
make it. Thus — 



4 


4 


4 


4 


4 


4 


4 


4 


4 




3 


6 


12 


24 


48 


96 


192 


384 


4 


7 


10 


16 


[28] 


52 


100 


196 


388 


3 


? 


© 


$ 


® 


2/ 


h 


¥ 


t{j 






(The characters below the numbers are the symbols of the 
planets, used in almanacs instead of their names.) 

This law seems to have been first noticed by Titius of Wittenberg, 
but bears the name of Bode, Director of the Observatory of Berlin, 
who first secured general attention to it. 

No logical reason can yet be given for it. It may be a mere con- 
venient coincidence, or it may be the result of the process of develop- 
ment which brought the solar system into its present state. 

220. Kepler's Laws. — Three famous laws discovered by 
Kepler (1607-1620) govern the motions of the planets : — 

I. The orbit of each planet is an ellipse with the sun in one 
of its foci. (See Appendix, Art. 429, for a description of the 
ellipse.) 

II. In the motion of each planet around the sun, the radius 
vector describes equal areas in equal times. (See Art. 121, 
Fig. 13, for illustration.) 

III. The squares of the periods of the planets are propor- 
tional to the cubes of their mean distances from the sun. This 
is known as the Harmonic Law. Stated as a proportion it 
reads : P* : P 2 2 : : Af : A 2 S , or in words : The square of the period 
of planet No. 1 : square of the period of planet No. 2 : : cube of 
the mean distance of planet No. 1 : cube of the mean distance of 
planet No. 2. Planets No. 1 and No. 2 are any pair of planets 
selected at pleasure. (For fuller illustration, see Appendix, 
Art. 430.) 

It was the discovery of this law which so filled Kepler with 
enthusiasm that he wrote, " If God has waited 6000 years for 
a discoverer, I can wait as long for a reader." 



162 GRAVITATION. [§ 22 1 

221. Gravitation. — When Kepler discovered these three 
laws he could give no reason for them — no more than we 
can now for Bode's law ; — but some sixty years later Xewton 
discovered that they all follow necessarily as the consequence 
of the law of gravitation, which he had discovered ; namely, 
that "every particle of matter in the universe attracts every 
other particle with a force that varies directly as the masses of the 
particles, and inversely as the square of the distance between 
them" It would take us far beyond our limits to attempt to 
show hoiv Kepler's laws follow from this, but they do. The 
only mystery in the case is the mystery of the "attraction" 
itself; for this word " attraction " is to be taken as simply 
describing an effect without in the least explaining it. 

Things take place as if the atoms had in themselves intelligence to 
recognize each other's positions, and power to join hands in some way, 
and pnll upon each other through the intervening space, whether it 
be great or small. But neither Xewton nor any one else supposes that 
atoms are really endowed with any such power, and the explanation 
of gravity remains to be found : very probably it is somehow involved 
in that constitution of the material universe which makes possible the 
transmission through space of light and heat, and electric and mag- 
netic forces. 

222. Sufficiency of Gravitation to explain the Planetary 
Motions. — We wish to impress as distinctly as possible upon 
the student one idea; this namely, that given a planet once in 
motion, nothing further than gravitation is required to explain 
perfectly all its motions forever after. Many half-educated 
people have an idea that some other force or mechanism must 
act to keep the planets going. This is not so : not a single 
motion in the whole planetary system has ever yet been de- 
tected for which gravitation fails to account. 

223. Map of the Orbits. — Fig. 43 shows the smaller orbits 
of the system (including the orbit of Jupiter) drawn to scale, 






223] 



SMALLER PLANETARY ORBITS. 



163 



the radius of the earth's orbit being taken as four-tenths of an 
inch. 

On this scale, the diameter of Saturn's orbit would be 7.4 inches 
that of Uranus would be 13.4 inches, and that of Neptune about two 




Fig. 43. — Plan of the Smaller Planetary Orbits. 

feet. The nearest fixed star, on the same scale, would be a mile and 
a quarter away. 

It will be seen that the orbits of Mercury, Mars, Jupiter, 
and several of the asteroids are quite distinctly "out of cen- 



164 INCLINATION OJ? THE UKB1TS. [§2-3 

tre " with respect to the sun. The orbits are so nearly cir- 
cular that there is no noticeable difference between their 
length and their breadth, but the eccentricity shows plainly 

in the position of the sun. 

224. Inclination of the Orbits. — The orbits are drawn as if 
they all lay on the plane of the ecliptic ; i.e.. on the surface of 
the paper. This is not quite correct. The orbit of the asteroid 
Pallas should be really tipped up at an angle of nearly 30°, 
and that of Mercury, which is more inclined to the ecliptic 
than the orbit of any other of the principal planets, is sloped 
at an angle of 7°. The inclinations, however, are so small 

(excepting the asteroids) 

cg- ^fig ~^^s — ^- = that they may be neg- 

/ <S^ !? *~^jP ^^^y\ l ec ^ e( i ^ or ordinary pur- 

B\- ~— ^^Sb^ - * 1 \Jjtfr — /^ poses. On the scale of 

^C^""* ^k$&*^ ^^^ ^ ie diagram. Neptune, 

which rises and falls the 
most of all with refer- 
ence to the plane of the 
ecliptic, would never be more than a third of an inch above 
or below the level of the paper. 

The line in which the plane of a planet's orbit cuts the 
plane of the earth's orbit at the ecliptic is called the Line of 
Xodes. Fig. 44 shows how the line of nodes and the inclina- 
tion of the two orbits are related. 

225. Geocentric Motions of the Planets; i.e.. their motions 
with respect to the earth regarded as the centre of observation. 

While the planets revolve regularly in nearly circular orbits 
around the sun. with velocities 1 which depend upon their dis- 
tance from it. the motions relative to the earth are very dif- 
ferent, being made up of the planet's real motion combined 

1 A planet's velocity in miles per second equals very nearly . 1^ — 

\ Distance 



Fig. 44. — Inclination and Line of Nodes. 



, 225] 



DIRECT AND RETROGRADE MOTION. 



165 







with the apparent motion due to that of the earth in her own 
orbit. 

If, for instance, we keep up observations, for a long time, of 
the direction of Jupiter as seen from the earth, at the same 
time watching the changes 
of its distance by measur- 
ing the alterations of the 
planet's apparent size as 
seen in the telescope, and 
then plot the results to get 
the form of the orbit of 
Jupiter with reference to 
the earth, we get a path 
like that shown in Fig. 45, 
which represents his mo- 
tion relative to the earth 
during a term of about 
twelve years. The appear- 
ances are all the same as if 
the earth were really at rest while the planet moved in this 
odd way. 

The procedure for finding this relative orbit of Jupiter is the same 
as that indicated in Appendix, Art. 428, for finding the form of the 
earth's orbit around the sun. 

226. Direct and Retrograde Motion. — With the eye alone 
the changes in a planet's diameter would not be visible, and 
we should notice only the alternating direct (eastward) 
and retrograde (westward) motion of the planet among the 
stars. If we watch one of the planets (say Mars) for a few 
weeks, beginning at the time when it rises at sunset, we shall 
find that each night it has travelled some little distance to the 
west ; and it will keep up this westward or retrograde motion 
for some weeks, when it will stop or become "stationary," and 
will then reverse its motion and begin to move eastward. If 



Fig. 45. 
Apparent Geocentric Motion of Jupiter. 



166 



ELONGATION AND CONJUNCTION. 



[§226 



we watch long enough (i.e., for several years) we shall find 
that it keeps up this oscillating motion all the time, the length 
of its eastward swing being always greater than that of the 
corresponding westward one. All the planets, without excep- 
tion, behave alike in this respect, as to their alternate direct 
and retrograde motion among the stars. 

227. Elongation and Conjunction. — The visibility of a 
planet does not, however, depend upon its position among 



Conjunction 




Greatest E. Elmigation 



Greatest W. Elongation 



Opposition 
Fig. 46. —Planetary Configurations. 

the stars, but upon, its position in the sky with reference to 
the sun's place. If it is very near the sun, it will be above 
the horizon only by day, and generally we cannot see it. The 
Elongation of a planet is the apparent distance from the sun 
in degrees, as seen from the earth, of course. In Fig. 46, for 
the planet P, it is the angle PES. When the planet is in line 



§ 227] SYNODIC PERIOD. 167 

with the sun as seen from the earth, at B, C, or / in the figure, 
the elongation is zero, and the planet is said to be in conjunc- 
tion; inferior conjunction, if the planet is between the earth 
and the sun, as at /; superior, if beyond the sun, as at B or. C. 
When the elongation is 180°, as at A, the planet is said to be 
in opposition. When the planet is at an elongation of 90°, as 
at F or (?, it is in quadrature. Evidently only those planets 
which lie within the earth's orbit, and are called 'inferior' 
planets, can have an inferior conjunction; and only those 
which are outside the earth's orbit (the superior planets) can 
come to quadrature or opposition. 

228. 'Synodic Period. — The synodic period of a planet is 
the time occupied by it in passing from conjunction to con- 
junction again, or from opposition to opposition; so called 
because the word " synod " is derived from two Greek words 
which mean i a coming together.' The relation of the synodic 
period to the sidereal is the same for planets as in the case of 
the moon. If E is the length of the true (sidereal) year, and 
P the planet's period, S being the length of the synodic period, 
then 

1 = 1-1 

SEP 

(The difference between — and — is to be taken without regard 

E P 

to which of the two is the larger.) 

229. The Synodic Motion, or Apparent Motion of a Planet 
with respect to < Elongation ' or to the Sun's Place in the Sky. 

— In this respect there is a marked difference between the 
superior and inferior planets. 

(a) The inferior planets are never seen very far from the 
sun, but appear to oscillate back and forth in front of and 
behind him. Venus, for instance, starting at superior con- 
junction at C (Tig, 46), seems to come out eastward from the 



168 PTOLEMAIC AND COPERN1CAN SYSTEMS. [§ 229 

sun as an evening star, until, at the point V, she reaches her 
greatest eastern elongation, about 47° from the sun. Then she 
begins to diminish her elongation, and approaches the sun, 
until she comes to inferior conjunction, at I. From there 
she continues to move westward as morning star, until she 
comes to V, her greatest western elongation, and there she 
begins to diminish her western elongation until, at the end 
of the synodic period, she is back at superior conjunction. 
The time taken to move from V to V through C is, in her 
case, more than three times that required to slide back from 
V to V 1 through J. The gain of eastern elongation is up-hill 
work, as she is then, so to speak, pursuing the sun, which 
itself moves eastward' nearly a whole degree every d£y along 
the ecliptic. 

(b) The superior planets may be found at all elongations, 
and do not oscillate back and forth with reference to the 
apparent place of the sun, but continually increase their 
western elongation or decrease their eastern. They always 
come to the meridian earlier on each successive night, though the 
difference is not uniform. 

230. Ptolemaic and Copernican Systems. — Until the time 
of Copernicus (about 1540) the Ptolemaic System prevailed 
unchallenged. It rejected the idea of the earth's rotation 
(though Ptolemy accepted the rotundity of the earth), placing 
her at the centre of things and teaching that the apparent 
motions of the stars and planets were real ones. It taught 
that the celestial sphere revolves daily around the earth, carry- 
ing the stars and planets with it, and that besides this diurnal 
motion, the moon, the sun, and all the planets revolve around 
the earth within the sphere, the two former steadily, but the 
planets with the peculiar looped motion shown in Fig. 45. 

Copernicus put the sun at the centre, and made the earth 
revolve on its axis and travel around the sun, and showed that 
it was possible in this simple way to account for all the other- 



§ 230] THE PLANETS THEMSELVES. 169 

wise hopelessly complicated phenomena of the planetary and 
diurnal motions, so far as then known. It was not until after 
the invention of the telescope, and the introduction of new 
methods of observation, that the facts which absolutely demon- 
strate the orbital motion of the earth were brought to light ; 
viz., Aberration of Light (Appendix, Art. 435) and Stellar 
Parallax (Art. 433). 

THE PLANETS THEMSELVES. 

231. In studying the planetary system we meet a number 
of inquiries which refer to the planet itself and not to its 
orbit ; relating, for instance, to its magnitude ; its mass, density, 
and surface-gravity; its diurnal rotation and oblateness ; its 
brightness, phases, and reflecting power, or "albedo"; the pecul- 
iarities of its spectrum; its atmosphere ; its surface-markings and 
topography ; and, finally, its satellite system, 

232. Magnitude. — The size of a planet is found by measur- 
ing its apparent diameter (in seconds of arc) with some form 
of "micrometer" (see Appendix, Art. 415). Since we can 
find the distance of a planet from the earth at any moment 
when we know its orbit, this micrometric measure will give us 
the means of finding at once the planet's diameter in miles. 

If we take r to represent the number of times by which the 
planet's semi-diameter exceeds that of the earth, then the area 
of the planet's surface compared with that of the earth equals 
r 2 , and its volume or bulk equals r 3 . The nearer the planet, 
other things being equal, the more accurately r and the quanti- 
ties to be derived from it can be determined. An error of 0".l 
in measuring the apparent diameter of Venus, when nearest us, 
counts for less than thirteen miles ; while in Neptune's case, 
the same error would correspond to more than 1300 miles. 

233. Mass, Density, and Gravity. — If the planet has a 
satellite, its mass is very easily and accurately found from the 



170 THE ROTATION PERIOD. [§ 233 

following proportion, which we simply state without demon- 
stration (see General Astronomy, Arts. 536, 539) ; viz. : — 

4 3 a 3 
Mass of Smi : mass of Planet : : — : — , 

in which A is the mean distance of the planet from the sun and 
T its sidereal period of revolution, while a is the distance of 
the satellite from the planet, and t its sidereal period ; whence 

Mass of Planet = Sun x ( — X — 

\t 2 A 

Substantially the same proportion may be used to compare the 
planet with the earth; viz. : — 

(Earth + Moon) : (Planet + Satellite) : : ?L : 2l, 

#! and t x being here the period and distance of the moon, and a 2 and 
t 2 those of the planet's satellite. 

If the planet has no satellite, the determination of its mass is a dif- 
ficult matter, depending upon perturbations produced by it in the 
motions of the other planets. 

Having the planet's mass compared with the earth, we get 
its density by dividing the mass by the volume, and the super- 
ficial gravity is found by dividing by r 2 the mass of the planet 
compared with that of the earth. 

234. The Rotation Period and Data connected with it. — 

The length of the planet's day, when it can be determined at 
all, is ascertained by observing with the telescope some spot 
on the planet's disc and noting the interval between its returns 
to the same apparent position. The inclination of the planet's 
equator to the plane of its orbit, and the position of its equi- 
noxes, are deduced from the same observations that give the 
planet's diurnal rotation ; we have to observe the path pursued 
by a spot in its motion across the disc. Only Mars, Jupiter, 
and Saturn permit us to find these elements with any consider- 
able accuracy. 

The ellipticity or oblateness of the planet, due to its rota- 



§234] SATELLITE SYSTEM. 171 

tion, is found by taking measures of its polar and equatorial 
diameters. 

235. Data relating to the Planet's Light. — A planet's 
brightness and its reflecting power, or " albedo," are deter- 
mined by photometric observations, and the spectrum of the 
planet's light is of course studied with the spectroscope. The 
question of the planet's atmosphere is investigated by means of 
various effects upon the planet's appearance and light, and by 
the phenomena that occur when the planet comes very near to 
a star or to some other heavenly body which lies beyond. The 
planet's surface-markings and topography are studied directly 
with the telescope, by making careful drawings of the appear- 
ances noted at different times. Photography, also, is begin- 
ning to be used for the purpose. If the planet has any well- 
marked and characteristic spots upon its surface by which the 
time of rotation can be found, then it soon becomes easy to 
identify such as are really permanent, and after a time we can 
chart them more or less perfectly ; but we add at once that 
Mars is the only planet of which, so far, we have been able to 
make anything which can be fairly called a map. 

236. Satellite System. — The principal data to be ascer- 
tained are the distances and periods of the satellites. These 
are obtained by micrometric measures of the apparent distance 
and direction of each satellite from the planet, followed up for 
a considerable time. In a few cases it is possible to make 
observations by which we can determine the diameters of the 
satellites, and when there are a number of satellites together 
their masses may sometimes be ascertained from their mutual 
perturbations. With the exception of our moon and Iapetus, 
the outer satellite of Saturn, all the satellites of the solar sys- 
tem move almost exactly in the plane of the equator of the planet 
to which they belong ; at least, so far as known, for we do not 
know with certainty the position of the equators of Uranus 



172 • PLANETARY DATA. [§ 236 

and Neptune. Moreover, all the satellites, except the moon 
and Hyperion, the seventh satellite of Saturn, move in orbits 
that are practically circular. 

237. Tables of Planetary. Data. — In the Appendix we pre- 
sent tables of the different numerical data of the solar system, 
derived from the best authorities and calculated for a solar 
parallax of 8". 80, the sun's mean distance being, therefore, 
taken as 92,897.000 miles. These tabulated numbers, however, 
differ widely in accuracy. The periods of the planets and 
their distances in ' astronomical units ' are very accurately 
known ; probably the last decimal in the table may be trusted. 
Next in certainty come the masses of such planets as have 
satellites, expressed in terms of the sun's mass. The masses 
of Venus and Mercury are much more uncertain. 

The distances of the planets in miles, their masses in terms 
of the earth's mass, and their diameter in miles, all involve the 
solar parallax, and are affected by the slight uncertainty in its 
amount. For the remoter planets, diameters, volumes, and 
densities are all subject to a very considerable percentage of 
error. The student need not be surprised, therefore, at finding 
serious discrepancies between the values given in these tables 
and those given in others, amounting in some cases to ten or 
twenty per cent, or even more. Such differences merely indi- 
cate the actual uncertainty of our knowledge. Fig. 47 gives 
an idea of the relative sizes of the planets. 

The sun, on the scale of the figure, would be about a foot in 
diameter. 

238. Sir John Herschel's Illustration of the Dimensions of 
the Solar System. — In his "Outlines of Astronomy," Herschel 
gives the following illustration of the relative magnitudes and dis- 
tances of the members of our system : — 

* ' Choose any well-levelled field. On it place a globe two feet in diame- 
ter. This will represent the sun. Mercury will be represented by a grain 



§238] 



BELATIVE SIZE OF THE PLANETS. 



173 



of mustard seed on the circumference of a circle 164 feet in diameter for 
its orbit ; Venus*, a pea, on a circle of 284 feet in diameter ; the Earth, 
also a pea, on a circle of 430 feet ; Mars, a rather large pin's head, on a 
circle of 654 feet ; the asteroids, grains of sand, on orbits having a diame- 
ter of 1000 to 1200 feet ; Jupiter, a moderate- sized orange, on a circle 
nearly half a mile across ; Saturn, a small orange, on a circle of four- fifths 




Fig. 47. — Relative Size of the Planets. 

of a mile ; Uranus, a full-sized cherry or small plum, upon a circumfer- 
ence of a circle more than a mile in diameter ; and, finally, Neptune, a 
good- sized plum, on a circle about 2\ miles in diameter." 

We may add that, on this scale, the nearest star would be on the 
opposite side of the globe, 8000 miles away. 



THE TERRESTRIAL PLANETS, — MERCURY, VENUS, AND 

MARS. 

239. Mercury has been known from the remotest antiquity, 
and among the Greeks it had for a time two names, — Apollo 
when it was morning star, and Mercury when it was evening 
star. It is so near the sun that it is comparatively seldom 



174 MERCURY. [§ 239 

seen with the naked eye, but when near its greatest elongation 
it is easily enough visible as a brilliant reddish star of the 
first magnitude, low down in the twilight. It is best seen in 
the evening at such eastern elongations as occur in the spring. 
When it is morning star, it is best seen in the autumn. 

It is exceptional in the solar system in various ways. It is 
the nearest planet to the sun, receives the most light and heat, 
is the swiftest in its movement, and (excepting some of the 
asteroids) has the most eccentric orbit, with the greatest inclina- 
tion to the ecliptic. It is also the smallest in diameter (again 
excepting the asteroids), has the least mass, and (probably) 
the greatest density of all the planets. 

240. Its Orbit. — The planet's mean distance from the sun 
is 36,000000 miles, but the eccentricity of its orbit is so great 
(0.205) that the sun is 7,500000 miles out of the centre, 
and the distance ranges all the way from 28^- millions to 43^- 
millions, while the planet's velocity in the different parts of 
its orbit varies from 36 miles a second to only 23. A given 
area upon its surface receives on the average nearly seven 
times as much light and heat as it would on the earth ; but 
the heat received when the planet is at perihelion is 2\ times 
greater than at aphelion. For this reason there must be at 
least two seasons in its year, due to the changing distance of 
the planet from the sun, whatever may be the position of its 
equator or the length of its day. The sidereal period is 88 
days, and the synodic period (or time from conjunction to con- 
junction) is 116 days. The greatest elongation ranges from 
18° to 28°, and occurs about 22 days before and after the in- 
ferior conjunction. The inclination of the orbit to the ecliptic 
is about 7°. 

241. Planet's Magnitude, Mass, etc. — The apparent diam- 
eter of Mercury varies from 5" to about 13", according to its 
distance from us ; and its real diameter is very near 3000 



§241] TELESCOPIC APPEARANCE. 175 

miles. This makes its surface about one-seventh that of the 
earth, and its bulk or volume one-eighteenth. The planet's 
mass is very difficult to determine, since it has no satellite, 
and it is not accurately known. Probably it is about one- 
twenty-seventh of the earth's mass; it is certainly smaller 
than that of any other planet (asteroids excepted). Our un- 
certainty as to the mass prevents us from assigning certain 
values to its density or superficial gravity, though it is prob- 
ably two-thirds as dense as the earth, and the foi*ce of gravity 
upon it is about one-quarter what it is upon the earth. 

242. Telescopic Appearances, Phases, etc. — Seen through 
the telescope the planet looks like a little moon, showing 




Fig. 48. — Phases of Mercury and Venus. 

phases precisely similar to those of our satellite. At inferior 
conjunction the dark side is towards us ; at superior conjunc- 
tion the illuminated surface. At greatest elongation, the 
planet appears as a half-moon. It is gibbous between superior 
conjunction and greatest elongation, while between inferior 
conjunction and greatest elongation it is crescent. Fig. 48 
illustrates these phases. 

The atmosphere of the planet cannot be as dense as that of 
the earth or Venus, because at a transit it shows no encircling 
ring of light, as Venus does (Art. 248) ; both Huggins and 
Vogel, however, report that the spectrum of the planet, in 



176 DIURNAL ROTATION OF MERCURY. [§242 

addition to the ordinary dark lines belonging to the spectrum 
of reflected sunlight, shows certain bands known to be due to 
water-vapor, thus indicating that water exists in the planet's 
atmosphere. 

Generally, Mercury is so near the sun that it can be observed 
only by day ; but when proper precautions are taken to screen 
the object-glass of the telescope from direct sunlight, the ob- 
servation is not especially difficult. The surface presents very 
little of interest. The disc is brighter at the edge than at the 
centre, but the markings are not well enough defined to give 
us any really satisfactory information as to its topography. 

The albedo, or reflecting power, of the planet is very low, 
only 0.13, somewhat inferior to that of the moon and very 
much below that of any other of the planets. No satellite is 
known, and there is no reason to suppose that it has any. 

243. Diurnal Rotation of the Planet. — In 1889, Schiaparelli, 
the Italian astronomer, announced that he had discovered cer- 
tain markings upon the planet, and that they showed that the 
planet rotates on its axis only once during its orbital period of 
eighty-eight days, thus keeping the same face always turned 
towards the sun, in the same way that the moon behaves with 
respect to the earth. Owing to the eccentricity of the planet's 
orbit, however, it must have a large libration (Art. 145), 
amounting to about 23|- on each side of the mean ; i.e., seen 
from a favorable station on the planet's surface, the sun, 
instead of rising and setting, as with us, would seem to oscil- 
late back and forth through an arc of 47° once in 88 days. 

This asserted discovery is very important and has excited 
great interest. Schiaparelli is probably correct, but it may be 
well to wait for confirmation of his observations by others 
before absolutely accepting the conclusion. 

244. Transits of Mercury. — At the time of inferior con- 
junction, the planet usually passes north or south of the sun, 



§ 244 ] VENUS. 177 

the inclination of its orbit being 7°; but if the conjunction 
occurs when the planet is very near its node (Art. 224), it 
crosses the sun's disc and becomes visible upon it as a small 
black spot ; not, however, large enough to be seen without a 
telescope, as Venus can under similar circumstances. Since 
the earth passes the planet's line of nodes on May 7th and 
Nov. 9th, transits can occur only near those days. 

The transits of the last half of the present century are as follows : 
May Transits.— May 6th, 1878 ; May 9th, 1891. November Tran- 
sits.— Nov. 12th, 1861; Nov. 5th, 1868; Nov. 7th, 1881; Nov. 
10th, 1894. The next transits will occur in Nov. 1907, and 1914 ; 
and in May, 1924. 

Transits of Mercury are of no particular astronomical importance, 
except as furnishing accurate determinations of the planet's place in 
the sky at a given time. 

VENUS. 

245. The second planet in order from the sun is Venus, the 
brightest and most conspicuous of all. It is so brilliant that 
at times it casts a shadow, and is easily seen by the naked eye 
in the daytime. Like Mercury it had two names among the 
Greeks, — Phosphorus as morning star, and Hesperus as even- 
ing star. 

Its mean distance from the sun is 67,200000 miles, and its 
distance from the earth ranges from 26,000000 miles (93 — 67) 
to 160,000000 (93 + 67). No other body ever comes so near 
the earth except the moon, and occasionally a comet. The 
eccentricity of the orbit of Venus is the smallest in the plane- 
tary system, only 0.007, so that the greatest and least dis- 
tances of the planet from the sun differ from the mean less 
than 500,000 miles. Its sidereal period is 225 days, or seven 
and a half months ; and its synodic period 584 days, — a year 
and seven months. From inferior conjunction to greatest 
elongation is only 71 days. The inclination of its orbit is not 
quite 3-|°, — less than half that of Mercury. 






178 MAGNITUDE, MASS, ETC. [§ 246 

246. Magnitude, Mass, Density, etc. — The apparent diam- 
eter of the planet varies from 67", at the time of inferior con- 
junction, to only 11", at superior ; the great difference arising 
from the enormous variation in the distance of the planet from 
the earth. The real diameter of the planet in miles is about 
7700. Its surface compared with that of the earth is -^ ; its 
volume, -j^-. By means of the perturbations she produces 
upon the earth, the mass of Venus is found to be a little less 
than four-fifths of the earth's mass, so that her mean density 
is a little less than the earth's. In magnitude she is the 
earth's twin sister. 

247. General Telescopic Appearance ; Phases, etc. — The 

general telescopic appearance of Venus is striking on account 
of her great brilliancy, but exceedingly unsatisfactory because 
nothing is distinctly outlined upon the disc. 

When about midway between greatest elongation and infe- 
rior conjunction, the planet has an apparent diameter of 40", 
so that with a magnifying power of only 45 she looks exactly 
like the moon four days old, and of the same apparent size. 
(Very few persons, however, would think so on the first view 
through the telescope ; the novice always underrates the 
apparent size of a telescopic object.) 

The phases of Venus were first discovered by Galileo in 1610, and 
afforded important evidence as to the truth of the Copernican system 
as against the Ptolemaic. Fig. 49 represents the planet's disc as seen 
at five points in its orbit. 1, 3, and 5 are taken at superior conjunc- 
tion, greatest elongation, and near inferior conjunction, respectively; 
while 2 and 4 are at intermediate points. (Xo. 2 is badly engraved, 
however ; the sharp corners are impossible.) 

The planet attains its maximum brightness when its appar- 
ent area is at a maximum, about thirty-six days before and 
after inferior conjunction. According to Zollner, the 'albedo' 
of the planet is 0.50; i.e., it reflects about half the light 
which falls upon it, the reflecting power being about three 



247] 



TELESCOPIC APPEARANCES OF VENUS. 



179 



times that of the moon, and almost four times that of Mer- 
cury. It is, however, slightly exceeded by the reflecting 
power of Uranus and Jupiter, while that of Saturn is about 




Fig. 49. — Telescopic Appearances of Venus. 

the same. This high albedo probably indicates a surface 
mostly covered with clouds, since few rocks or soils could 
match its brightness. Like Mercury, Mars, and the moon, the 
disc of Venus is brightest at the edge, — in contrast with the 
appearance of Jupiter and Saturn. 



248. Atmosphere of the Planet. — When the planet is near 
inferior conjunction, the horns of the crescent extend notably 
beyond the diameter ; and when very near conjunction, a thin 
line of light has been seen by some observers to complete the 
whole circumference of the disc. This is due to the refrac- 
tion of sunlight bent around the planet's globe by its atmos- 
phere, a phenomenon still better seen when the planet is 
entering upon the sun's disc at a transit. The black disc is 



180 



ATMOSPHERE OF VENUS. 



[§248 



then encircled by a delicate luminous ring, as illustrated by 
Fig. 50. The planet's atmosphere is probably from one and 

one-half to two times as 
dense as our own, and 
the spectrum shows 
evidence of water-va- 
por in it. Many ob- 
servers have also re- 
ported faint lights as 
visible at times on the 
dark portions of the 
planet's disc. These 
cannot be accounted 
for by any mere reflec- 
tion or refraction of 
sunlight, but must orig- 
inate on the planet it- 
self. They recall the 
Aurora Borealis and 
other electrical mani- 





Fig. 50. — Atmosphere of Venus as seen during a 
Transit. (Vogel, 1882.) 



testations on the earth, though it is impossible to give a certain 
explanation of them as yet. 



249. Surface-markings, Rotation, etc. — As has been said, 
Venus is a very unsatisfactory telescopic object. She pre- 
sents no obvious surface-markings, — nothing but occasional 
indefinite shadings : sometimes, however, when in the crescent 
phase, intensely bright spots have been reported near the 
points of the crescent, which may perhaps be " ice-caps" like 
those which are seen on Mars. The darkish shadings may 
possibly be continents and oceans, dimly visible, or they may 
be atmospheric objects ; observations do not yet decide. From 
certain irregularities occasionally observed upon the " termi- 
nator " (Art. 146), various observers have concluded that there 
are high mountains upon the planet. 






§ 249] TRANSITS. 181 

As to the rotation-period of the planet, nothing is yet cer- 
tainly known. The length of its day has been set, on very 
insufficient grounds, at about 23 hours and 21 minutes ; but the 
recent work of Schiaparelli makes it almost certain that this 
result cannot be trusted, and renders it rather probable that 
Venus behaves like Mercury in its diurnal rotation, the length 
of its sidereal day being equal to the time of its orbital revolu- 
tion. The planet's disc shows no sensible oblateness. 

Xo satellite has ever been discovered; not, however, for 
want of earnest searching. 

250. Transits. — Occasionally Venus passes between the 
earth and the sun at inferior conjunction, giving us a so- 
called " transit." She is then visible, even to the naked eye, 
as a black spot on the sun's disc, crossing it from east to w r est. 
When the transit is central it occupies about eight hours, but 
when the track lies near the edge of the disc the duration 
is correspondingly shortened. Since the earth passes the 
nodes of the orbit on June 5th and Dec. 7th, all the transits 
occur near these days, but they are ex- 
tremely rare phenomena. Their special 
interest consists in their availability for 
the purpose of finding the sun's parallax 
(see Appendix, Art. 437, and General 
Astronomy, Chap. XVI.). 

The first observed transit in 1639 was seen 
by only two persons, — Horrox and Crabtree in FlG - ol# 

_T , , , , ,, » i-ii i Transit of Venue's Tracks. 

England, — but the tour which have occurred 

since then have been observed in all parts of the world by scientific 
expeditions sent out for the purpose by the different governments. 
The transits of 1769 and 1882 were visible in the United States. 
Transits of Venus have occurred or will occur at the following 
dates : — 

j Dec. 7th, 1631. ( June 5th, 1761. 

( Dec. 4th, 1639. ( June 3d, 1769. 




182 MARS. |§200 



j D60. 9th, 

J Deo. 6th, 



!)(•(•. 9th, 1874. j June Bth, 2004. 

1882. 1 June 6th, 2012. 



Fig, 61 .shows the tracks of Venus across the sun's disc in the tran- 
sits of 1874 and 1882. 

MARS. 

251. This planet, also, has always been known, [t is so 
conspicuous on account of Its fiery red color and brightness, 
as well as the rapidity and apparent caprioiousness of lis 
movement among the stars, that it could not have escaped the 
notice of the very earliest observers. 

li,:; mean distance from the sun is a Little more than one and 
a half times that of the earth (141,500000 miles), and the ec- 
centricity of its orbit is so considerable (0.093) that its radius 
vector varies more than 26,000000 miles. At, opposition the 
planet's average distance from the earth is 48,600000 miles; 
but when opposition occurs near the planet's perihelion, this 
distance is reduced to less than 36,000000 miles, while near 
aphelion it is over 61,000000 miles. At conjunction the aver- 
age distance from the earth is 234,000000 miles. 

The apparent diameter and brightness oi* the planet of 

course vary enormously with these great changes of distance. 

At a favorable opposition (when the planet's distance from us 
is the least possible) it is more than fifty times as bright as at 

conjunction, and fairly rivals Jupiter; when most remote, it is 

hardly as bright as the Pole-star, 

The favorable oppositions ocean- always in fche latter part of August, 
and at intervals of fifteen or seventeen years. The Last suoh opposi- 
tion was in 1892, and the next will be Ln 1907. 

The inclination of fche orbit is small, L° 51'. The planet's 

Sidereal period is f>S7 days (one year, ten and a hall* months); 

its synodic period is much fche Longest in fche planetary system, 

being 780 days, or nearly two years and two months. During 



§251] TELESCOPIC ASPECT. 183 

710 of these 780 days it moves towards the east, and retro- 
grades during 70. 

252. Magnitude, Mass, etc. — The apparent diameter of the 
planet ranges from 3". 6, at conjunction, to 25" at a favorable 
opposition. Its real diameter is approximately 4300 miles, 
with an error of perhaps 50 miles one way or the other. 
This makes its surface about two-sevenths, and its volume 
one-seventh of the earth's. Its mass is a little less than one- 
ninth of the earth's mass, its density 0.73, and its superficial 
gravity 0.38 ; i.e., a body which here weighs 100 pounds would 
have a weight of only 38 pounds on the surface of Mars. 

253. General Telescopic Aspect, Phases, etc. — When the 
planet is nearest, it is more favorably situated for telescopic 
observation than any other heavenly body, the moon alone 
excepted. It then shows a ruddy disc, 
which, with a magnifying power of 75, 
is as large as the moon. Since its orbit 
is outside the earth's, it never exhibits 
the crescent phases like Mercury and 
Venus; but at quadrature it appears 
distinctly gibbous, as in Fig. 52, about 
like the moon three days from full. Like 
Mercury, Venus, and the moon, its disc 
is brightest at the limb (i.e., at its circu- ,- ™ 

° \ ; Mare at Quadrature. 

lar edge) ; but at the " terminator," or 
boundary between day and night upon the planet's surface, 
there is a slight shading, which, taken in connection with cer- 
tain other phenomena, indicates the presence of an atmosphere. 
This atmosphere, however, is probably much less dense than 
that at the earth, as indicated by the infrequency of clouds 
and of other atmospheric phenomena familiar to us on the 
earth. Huggins and Vogel have reported that the planet's 
spectrum shows the lines of water-vapor, but the recent obser- 




Fig. 52. 



184 MARS. [§253 

vations of Campbell at the Lick Observatory do not confirm 
this, and go to show that whatever atmosphere exists must be 
very rare indeed, probably not more than one-fourth as dense 
as our own. 

Zollner gives the albedo of Mars as 0.26, just double that of 
Mercury, and much higher than that of the moon, but only 
about half that of Venus and the major planets. Near oppo- 
sition the brightness of the planet suddenly increases in the 
same way as that of the moon near the full (Art. 149). 

254. Rotation, etc. — The spots upon the planet's disc 
enable us to determine its period of rotation with great pre- 
cision. Its sidereal day is found to be 24 hours, 37 minutes, 
22.67 seconds, with a probable error not to exceed one-fiftieth 
of a second. It is the only one of the planets which has the 
length of its day determined with any such accuracy. The 
exactness is obtained by comparing the drawings of the planet 
made two hundred years ago with others made recently. 

The inclination of the planet's equator to the plane of its 
orbit is very nearly 24° 50' (26° 21 f to the ecliptic). So far, 
therefore, as depends upon that circumstance, Mars should 
have seasons substantially the same as our own, and certain 
phenomena make it evident that such is the case. 

The planet's rotation causes a slight flattening of the poles, 
— hardly sensible to observation, but probably about $^. 
(Larger values, now known to be erroneous, are given in 
many text-books.) 

255. Surface and Topography. — With even a small tele- 
scope, not more than four or five inches in diameter, the planet 
is a very beautiful object, showing a surface diversified with 
markings, light and dark, which for the most part are found to 
be permanent. Occasionally, however, we see others of a tem- 
porary character, supposed to be clouds ; but these are sur- 
prisingly rare, compared with clouds upon the earth. Tho 






§ 265 1 SCHIAPARELLl's OBSERVATIONS. 185 

permanent markings are broadly divisible into three classes : — 
First, the white patches, two of which are specially con- 
spicuous near the planet's poles, and are generally supposed 
to be masses of snow or ice, since they behave just as would 
be expected if such were the case. The northern one dwin- 
dles away during the northern summer, when the north pole is 
turned towards the sun, while the southern one grows rapidly 
larger ; and vice versa during the southern summer. 

Second, patches of bluish gray or greenish shade, covering 
about three-eighths of the planet's surface, and generally sup- 
posed to be bodies of water, though this is very far from certain. 
Third, extensive regions of various shades of orange and 




Fig. 53. — Telescopic Views of Mars. 

yellow, covering nearly five-eighths of the surface, and inter- 
preted as land. 

These markings, of course, are best seen when near the 
centre of the planet's disc ; near the limb they are lost in the 
brilliant light which there prevails, and at the terminator they 
fade out in the shade. Fig. 53 gives an idea of the planet's 
general appearance, though without pretending to minute 
accuracy. 

256. Recent Discoveries. The Canals and their Gemination. 

— In addition to these three classes of markings, the Italian 
astronomer Schiaparelli, in 1877 and 1879, announced the dis- 
covery of a great number of fine, straight lines, or " canals," 
as he called them, crossing the ruddy portions of the planet's 



186 RECENT DISCOVERIES. [§ 256 

surface in various directions ; and in 1881 he announced that 
many of them become double at times. For several years 
there was a suspicion that he was perhaps misled by some 
illusion, because other observers, with telescopes more power- 
ful than his, were unable to make out anything of the sort. 
More recently, however, his results have been abundantly 
confirmed both in Europe, and in this country at the Lick 
Observatory, and the observatory of Mr. Lowell in Arizona. 
It appears that the power of the telescope is not so important 
in the observation of these objects as steadiness of the air and 
keenness of the observer's eye : nor are they usually best 
seen when Mars is nearest, but their visibility depends upon 
the season on the planet ; and this is especially the case with 
their " gemination." 

As to their real nature there is wide difference of opinion, 
and it is doubtful if the true explanation has yet been pro- 
posed. According to Mr. Lowell, the polar caps are really 
snow masses, which melt in the (Martian) spring, and the 
water makes its way towards the equator, over the planet's 
mountainless plains, for several weeks obscuring the well- 
known markings which are visible at other times. For him 
the dark portions of the planet's surface are not seas, but 
land covered with vegetation of some sort, while the ruddy 
portions are rocky deserts intersected with the " canals," 
which, in his view, are really irrigating water-courses ; and on 
account of their straightness he is disposed to accept them as 
artificial. When the waters reach these canals, vegetation 
springs up along their banks on either side, and these streaks 
of vegetation are what we see. Where the water-courses 
cross each other there are dark, round " lakes," as they have 
been called, which he interprets as oases. 

Of course the difficulties of the theory are obvious : for 
instance, the almost absolute levelness of the planet's surface 
which it assumes, and especially the fact that at Mars the 
solar radiation is only half as intense as upon the earth. 
This, recalling the low density of his atmosphere, would 



§ 266] DECENT DISCOVERIES. 187 

naturally lead to the supposition that the temperature even at 
his equator must be lower than that at the summits of our 
highest mountains, and far below the freezing point of water. 
It was this consideration that has led some astronomers to 
suggest that the polar caps are not ice-sheets at all, but 
formed of congealed carbon-dioxide (C 2 ), or some substance 
of similar properties. 

But whatever the explanation may be, there is no longer 
any doubt that the " canals " are real, and that they, and the 
surface in general, undergo noticeable changes of appearance 
with the progress of the planet's seasons. At the same time 
Professor Holden of the Lick Observatory says that during 
the years 1888-1895 nothing has been observed there, so far 
as he knows, which goes to confirm Mr. Lowell's "very posi- 
tive and striking conclusions." The day may perhaps come 
when photography will be able to lend its aid to the solution 
of the problem, or some heat-measurer may be contrived 
sensitive enough to give us positive information as to the 
planet's temperature. If the polar caps are really snow caps, 
Mars must obtain surface heat from some still unexplained 
supply. 

257. Maps of the Planet. — A number of maps of Mars have 
been constructed by different observers since the first one was made 
by Maedler in 1830. Fig. 54 is reduced from one which was published 
in 1888 by Scbiaparelli, and shows most of his " canals " and their 
" geminations.' ' While there may be some doubt as to the accuracy 
of the minor details, there can be no doubt that the main features of 
the planet's surface are substantially correct. The nomenclature, 
however, is in a very unsettled state. Schiaparelli has taken his 
names mostly from ancient geography, while the English areogra- 
phers, 1 following the analogy of the lunar maps, have mainly used the 
names of astronomers who have contributed to our knowledge of the 
planet's surface. 



1 The Greek name of Mars is Ares; hence "Areography" is the de- 
scription of the surface of Mars. 



188 



CHART OF MARS. 



[§ 258 




§ 258] HABITABILITY OF MARS. 189 

258. Satellites. — The planet has two satellites, discovered 
by Professor Hall, at Washington, in 1877. They are ex- 
tremely small ; and observable only with very large telescopes. 
The outer one, Deirnos, is at a distance of 14,600 miles from 
the planet's centre, and has a sidereal period of 30 hours, 18 
minutes ; while the inner one, Phobos, is at a distance of only 
5800 miles, and its period is only 7 hours, 39 minutes, — less 
than one-third of the planet's day. (This is the only case of a 

. satellite with a period shorter than the day of its primary.) 
Owing to this circumstance, it rises in the west, as seen from 
the planet's surface, and sets in the east, completing its 
strange, backward, diurnal revolution in about eleven hours. 
Deimos, on the other hand, rises in the east, but takes nearly 
132 hours in its diurnal circuit, which is more than four of its 
months. Both the orbits are sensibly circular, and lie very 
closely in the plane of the planet's equator. 

Micronietric measures of the diameters of such small objects are im- 
possible; but from photometric observations, Professor E. C. Pick- 
ering, assuming that they have the same reflecting power as that of 
Mars itself, estimates the diameter of Phobos as about seven miles, 
and that of Deimos as five or six. According to this, Phobos, at the 
time of full moon, as seen from the planet's surface, would have an 
apparent diameter of about one-fifth that of our moon, and would 
probably give about one-fiftieth as much light. Deimos would be 
hardly more than a brilliant star, like Venus. 

259. Habitability of Mars. — As to this question, we can only 
say that, while the conditions on Mars are certainly very different 
from those prevailing on the earth, the difference is less than in the 
case of any other heavenly body which we can see with our present 
means of observation ; and if life, such as we know life upon the 
earth, can exist upon any of them, Mars is the place. But there is 
at present no scientific ground for belief one way or the other as to 
the habitability of " other worlds than ours," passionately as the 
doctrine has been affirmed and denied by men of opposite opinions. 



190 THE ASTEROIDS. [§ 260 



CHAPTER IX. 

THE PLANETS CONTINUED. 

THE ASTEROIDS. — INTRA-MERCURIAN PLANETS AND THE- 
ZODIACAL LIGHT. — THE MAJOR PLANETS, JUPITER, 
SATURN, URANUS, AND NEPTUNE. 

THE ASTEROIDS, OR MINOR PLANETS. 

260. The asteroids 1 are a multitude of small planets cir- 
cling around the sun in the space between Mars and Jupiter. 
It was early noticed that between Mars and Jupiter there is a 
gap in the series of planetary distances, and when Bode's Law 
(Art. 219) was published in 1772, the impression became very 
strong that there must be a missing planet in the space, — an 
impression greatly strengthened when Uranus was discovered 
in 1781, at a distance precisely corresponding to that law. 

The first member of the group was found by the Sicilian as- 
tronomer, Piazzi, on the very first night of the present century 
(Jan. 1, 1801). He named it Ceres, after the tutelary divinity 
of Sicily. The next year Pallas was discovered by Olbers. 
Juno was found in 1804 by Harding, and in 1807 Olbers, who 
had broached the theory of an exploded planet, discovered the 
fourth, Vesta, the only one which is bright enough ever to be 
easily seen by the naked eye. The search was kept up for 
some years longer, but without success, because the searchers 

1 They were first called "asteroids" (i.e., u star-like" bodies) by Sir 
William Herschel early in the century, because, though really planets, 
the telescope shows them only as stars, without a sensible disc. 



§ 260] ORBITS OF THE ASTEROIDS. 191 

did not look for small enough objects. The fifth asteroid 
(Astrsea) was found in 1845 by Hencke, an amateur who had 
resumed the subject by studying the fainter stars. In 1847 
three more were discovered, and every year since then has 
added from one to thirty. They are usually designated by 
their " numbers/' but all the older ones also have names : 
thus, Ceres is ®, Thule is (279), etc. In May, 1895, the list 
included 401 duly "numbered," besides about half a dozen 
more to which no number could be assigned, because they had 
not then been sufficiently observed to make it certain that 
they were not old ones rediscovered : for of the older ones 
eight or nine are now " adrift," i.e., they have not been 
observed for many years, and we do not know exactly their 
present position. Since 1891 the catalogue has been growing 
with rather inconvenient rapidity on account of the substitu- 
tion of photography for the old-fashioned method of planet- 
hunting. A large camera is strapped on the back of a 
telescope driven by clock-work, and a negative, covering from 
5° to 10° square of the heavens, is taken with an exposure of 
several hours. The thousands of stars that appear upon the 
plate all show neat, round discs, if the observer has kept his 
telescope steadily pointed ; but if there is a planet anywhere 
in the field it will move quite perceptibly during the long 
exposure, and its image upon the plate will be, not a dot, but 
a streak, which can be recognized at a glance. Sometimes 
three or four planets thus " show up " upon a single plate, — 
old ones as well as new of course ; but a few nights' observa- 
tion will usually furnish data from which the orbits can be 
computed with sufficient accuracy to decide all doubtful ques- 
tions. Wolf of Heidelberg, who first introduced the method, 
and Charlois of Nice, have been especially successful in this 
kind of asteroid-hunting. Among the old-fashioned planet- 
hunters Palisa of Vienna took the lead as the discoverer 
of 71 ; the late Dr. Peters of Clinton, N. Y., stood second 
with 48. 



192 THEIR ORBITS. [§ 261 

261. Their Orbits. — The mean distances of the different 
asteroids from the sun differ pretty widely, and the periods, 
of course, correspond. Medusa, (Hi), is probably the nearest 
to the sun of those at present known, its distance being 2.13 
(astronomical units), or 198,000000 miles, with a period of 
3 years and 40 days. Brucia, (323), may, however, have a 
period shorter by a day or two. Thule, (279), is the most 
remote, with a mean distance of 4.30 (400,000000 miles) and 
a period only 10 days less than 9 years. 

The inclinations of the orbits to the ecliptic average nearly 
8°. The orbit of Pallas, (2), is inclined at an angle of 35°, 
and seven others exceed 25°. The eccentricity of the orbits is 
very large in many cases. Aethra, (132) (one of the eight or 
nine that are adrift) has the largest eccentricity (0.38), and 
ten others have an eccentricity exceeding 0.30. It should be 
noted that the orbits of these planets are subject to very great 
" disturbances " from the attraction of Jupiter, and this makes 
the calculation of their motions much more laborious than 
that of the larger planets. Very few of them, therefore, are 
followed up closely ; only those that for some reason or other 
possess a special interest at some given time. 

262. The Bodies Themselves. — The four first discovered, 
and one or two others, when examined with a powerful 
telescope, show discs that are perceptible, but too small for 
satisfactory measurement with ordinary telescopes. By pho- 
tometric observations, assuming — what is by no means certain 
— that their albedo is about the same as that of Mars, it has 
been estimated that Vesta, the brightest, has a diameter of 
about 320 miles, and that the other three of the first four 
may be two-thirds as large. In 1895, however, Mr. Barnard 
of the Lick Observatory measured the diameters of Ceres, 
Pallas and Vesta, micrometrically, and obtained results that 
differ from these very widely, and should probably be pre- 
ferred. He finds Ceres to be the largest, with a diameter of 
488 miles. For Pallas, Vesta and Juno he gets diameters of 



§ 262] THE BODIES THEMSELVES. 193 

304, 248 and 118 miles respectively. As this work was done 
with a " double -image " micrometer, which avoids irradiation, 
the results are more reliable than his measures of Jupiter and 
Saturn, quoted later. ]STone of the rest can well exceed 100 
miles in diameter ; and the more newly discovered ones, which 
are just fairly visible in a telescope with an aperture of 10 or 
12 inches, cannot be many times larger than the moons of 
Mars, — say from 10 to 20 miles in diameter. 

As to the individual masses and densities, we have no 
certain knowledge. 

Assuming the correctness of Barnard's measures, and that the 
density of Ceres is about the same as that of the rocks which com- 
pose the earth's crust, her mass may be as great as IIF ^ that of the 
earth. If so, gravity on her surface would be about -^ of gravity 
here, so that a body would fall about twelve inches in the first 
second. Of course, on the smaller asteroids it would be much less. 

From the perturbations of Mars, Leverrier has estimated 
that the aggregate mass of the whole swarm cannot exceed 
one-fourth the mass of the earth, — something more than double 
that of Mars. 

The united mass of those at present known would make only a 
small fraction of such a body, — hardly a thousandth of it; prob- 
ably, however, those still undiscovered are very numerous. 

263. Origin. — As to this we can only speculate. It is 
hardly possible to doubt, however, that this swarm of little 
rocks in some way represents a single planet of the " terres- 
trial" group. A commonly accepted view is that the mate- 
rial, which, according to the nebular hypothesis, once formed 
a ring (like one of the rings of Saturn), and ought to have col- 
lected to make a single planet, has failed to be so united ; and 
the failure is ascribed to the perturbations produced by the 



194 INTRA-MEKCTJTtlAK PLAKETS. tS 26S 

next neighbor, the giant Jupiter, whose powerful attraction is 
supposed to have torn the ring to pieces, and thus prevented 
its normal development into a planet. 

Another view is that the asteroids may be fragments of an 
exploded planet. If so, there must have been not one, but 
many, explosions, first of the original body, and then of the 
separate pieces; for it is demonstrable that no single explo- 
sion could account for the present tangle of orbits. 



INTRA-MERCURIAN PLANETS AND THE ZODIACAL 
LIGHT. 






264. Intra-Mercurian Planets. — It is very possible, indeed not 
improbable, that there is a considerable quantity of matter circu- 
lating around the sun inside the orbit of Mercury. This is suggested 
by an otherwise unexplained perturbation of its orbit. It has been 
somewhat persistently supposed that this intra-Mercurian matter is 
concentrated into one, or possibly two, planets of considerable size, 
and such a planet has several times been reported as discovered, and 
has even been named Vulcan. The supposed discoveries have never 
been confirmed, however, and the careful observations of total solar 
eclipses during the past ten years make it practically certain that 
there is no " Vulcan." Possibly, however, there is a family of intra- 
Mercurian asteroids ; but they must be very minute, or some of them 
would certainly have been found either during eclipses or crossing the 
sun's disc ; a planet as much as 200 miles in diameter could hardly 
have escaped discovery. 

265. The Zodiacal Light. — This is a faint beam of light 
extending from the sun both ways along the ecliptic. In the 
evening it is best seen in the early spring, and in our latitude 
then extends about 90° eastward from the sun ; in the tropics, 
it is said that it can be followed quite across the sky. The 
region near the sun is fairly bright and even conspicuous, but 
the more distant portions are extremely faint and can be 
observed only in places where there is no illumination of the 



§ 266 1 JUPITER. 195 

air by artificial lights. Its spectrum is a simple, continuous 
spectrum, without markings of any kind, so far as can be 
observed. 

We emphasize this, because of late it has been mistakenly reported 
that the bright line which characterizes the spectrum of the Aurora 
Borealis appears in the spectrum of the zodiacal light. 

The cause of the phenomenon is not certainly known. Some 
imagine that the zodiacal light is only an extension of the 
solar corona (whatever that may be), which is not perhaps 
unlikely ; but on the whole the more prevalent opinion seems 
to be that it is due to sunlight reflected from myriads of small 
meteoric bodies circling around the sun, nearly in the plane of 
the ecliptic, thus forming a thin, flat sheet (something like one 
of Saturn's rings), which extends far beyond the orbit of the 
earth. 

THE MAJOR PLANETS.— JUPITER. 

266. Jupiter, the nearest of the major planets, stands next 
to Venus in the order of brilliance among the heavenly bodies, 
being fully five or six times as bright as Sirius, and decidedly 
superior to Mars, even when Mars is nearest. It is not, like 
Venus, confined to the twilight sky, but at the time of opposi- 
tion dominates the heavens all night long. 

Its orbit presents no marked peculiarities. The mean dis- 
tance of the planet from the sun is a little more than five astro- 
nomical units (483,000000 miles), and the eccentricity of the 
orbit is not quite ■£$, so that the actual distance ranges about 
21,000000 miles each side of the mean. At an average oppo- 
sition, the planet's distance from the earth is about 390,000000 
miles, while at conjunction it is distant about 580,000000. 

The inclination of its orbit to the ecliptic is only 1° 19'. Its 
sidereal period is 11.86 years, and the synodic is 399 days (a 
figure easily remembered), — a little more than a year and a 



196 DIMENSIONS, MASS, ETC. [§ 26 ^ 

month ; i.e., each year Jupiter comes to opposition a month 
and four days later than in the preceding year. 

267. Dimensions, Mass, Density, etc. — The planet's appar- 
ent diameter varies from 50" to 32 ", according to its distance 
from the earth. The disc, however, is distinctly oval, so that 
while the equatorial diameter is 88,200 miles, the polar diam- 
eter is only 83,000. The mean diameter (see Art. 112) is 
86,500 miles, or very nearly eleven times that of the earth. 1 

Its surface, therefore, is 119, and its volume or bulk 1300 
times that of the earth. It is by far the largest of all the 
planets, — larger, in fact, than all the rest united. 

Its mass is very accurately known, both by means of its 
satellites and from the perturbations it produces upon certain 
asteroids. It is y-^Vs of the sun's mass, or about 316 times 
that of the earth. 

Comparing this with its volume, we find its mean density to 
be 0.24; i.e., less than one-fourth the density of the earth, and 
almost precisely the same as that of the sun. Its surface 
gravity is about 2| times that of the earth, but varies nearly 
20 per cent between the equator and poles of the planet on 
account of the rapid rotation. 

268. General Telescopic Aspect, Albedo, etc. — In a small 
telescope the planet is a fine object ; for a magnifying power 
of only 60 makes its apparent diameter, even when remotest, 
equal to that of the moon. With a large instrument and a 
magnifying power of 200 or 300, it is magnificent, the disc 
being covered with an infinite variety of detail, interesting in 
outline and rich in color, changing continually as the planet 
turns on its axis. For the most part the markings are 

1 A series of measures made by Barnard in 1893 with the Lick tele- 
scope, gives an equatorial diameter of 90,190 miles, and a polar diameter 
of 34,560 ; but these figures probably need a correction for irradiation. 



§268] 



TELESCOPIC VIEWS OF JUPITER. 



197 



arranged in " belts " parallel to the planet's equator, as shown 
in Fig. 55. 

The left-hand one of the two larger figures is from a drawing by 
Trouvelot (1870), and the other from one by Vogel (1880). The 
smaller figure below represents the planet's ordinary appearance in 
a three-inch telescope. 

Near the limb the light is less brilliant than in the centre of 
the disc, and the belts there fade out. The planet shows no 




Fig. 55. — Telescopic Views of Jupiter. 



perceptible phases, but the edge which is turned away from 
the sun is usually sensibly darker than the other. According 
to Zollner, the mean albedo of the planet is 0.62, which is ex- 
tremely high, that of white paper being only 0.78. The ques- 
tion has been raised whether Jupiter is not to some extent 



198 JUPITER. [§ 268 

self-luminous, but there is do proof and little probability that 
such is the case. 



269. Atmosphere and Spectrum. — The planet's atmosphere 
must be very extensive. The forms which we see with the 
telescope are all evidently atmospheric. In fact, the low mean 
density of the planet makes it very doubtful whether there is 
anything solid about it anywhere, — whether it is anything 
more than a ball of fluid overlaid by cloud and vapor. 

The spectrum of the planet differs less from that of mere 
reflected sunlight than might have been expected, showing 
that the light is not obliged to penetrate the atmosphere to 
any great depth before it encounters the reflecting envelope of 
cloud. There are, however, certain unexplained dark shadings 
in the red and orange parts of the spectrum that are prob- 
ably due to the planet's atmosphere, and seem to be identical 
in position with certain bands which, in the spectra of Uranus 
and Neptune, are much more intense. 

270. Rotation. — Jupiter rotates on its axis more swiftly 
than any other of the planets. Its sidereal day has a length 
of about 9 hours, 55 minutes, but the time can be given only 
approximately, because different results are obtained from dif- 
ferent spots, according to their nature and their distance from 
the equator, — the differences amounting to six or seven min- 
utes. Speaking generally, spots near the equator indicate a 
shorter period of rotation than those near the poles, just as is 
the case with the sun. White spots also make the circuit 
quicker than dark spots near them. 

In consequence of the swift rotation, the planet's oblateness 
or " polar compression" is quite noticeable, — about T a T . The 
inclination of the planet's equator to its orbit is only 3°, so 
that there can be no well-marked seasons on the planet due to 
such causes as our own seasons. 



§271] PHYSICAL CONDITION — SATELLITES. 199 

271. Physical Condition. — This is obviously very different 
from that of the earth or Mars. No permanent markings are 
found upon the disc, though occasionally there are some which 
may be called " sub-permanent " as, for instance, the great 
red spot shown in Fig. 55. This was first noticed in 1878, 
became extremely conspicuous for several years, and still 
(1895) remains visible as a faded ghost of itself. Were it 
not that during the years of its visibility it has changed the 
length of its apparent rotation by about six seconds (from 9 
hours, 55 minutes, 34.9 seconds to 9 hours, 55 minutes, 40.2 
seconds), we might suppose it permanently attached to the 
planet's surface, and evidence of a coherent mass underneath. 
As it is, opinion is divided on this point ; the phenomenon is 
as puzzling as the canals of Mars. 

Many things in the planet's appearance indicate a high 
temperature, as, for instance, the abundance of clouds, and 
the swiftness of their transformations ; and since on Jupiter 
the solar light and heat are only -^ as intense as here, we are 
forced to conclude that it gets very little of its heat from the 
sun, but is probably hot on its own account, and for the same 
reason that the sun is hot ; viz., as the result of a process of 
condensation. In short, it appears very probable that the 
planet is a sort of semi-sun, — hot, though not so hot as to be 
sensibly self-luminous. 

272. Satellites. — Jupiter has five satellites, four of them 
large and easily seen with a very small telescope, while the 
fifth, discovered by Barnard in 1892, is extremely small and 
visible only in the largest instruments. 

The four large satellites were the first heavenly bodies ever 
discovered. Galileo found them in January, 1610, within a 
few weeks after the invention of his telescope. 

They are now usually known as the first, second, etc., in the 
order of their distance from the planet. The distances range 
from 262,000 to 1,169,000 miles, being respectively 6, 9, 15, 



200 SATELLITES OF JUPITER. [§ 2 ^2 

and 26 radii of the planet (nearly). Their sidereal periods 
range from 42 hours to 16| days. Their orbits are sensibly 
circular, and lie very nearly in the plane of the equator. The 
third satellite is much the largest, having a diameter of about 
3600 miles, while the others are between 2000 and 3000. 

For some reason, the fourth satellite is a very dark-complexioned 
body, so that when it crosses the planet's disc it looks like a black 
spot hardly distinguishable from its own shadow: the others, under 
similar circumstances, appear bright, dark, or invisible, according 
to the brightness of the part of the planet which happens to form 
the background. In Fig. 55 a satellite and its shadow are visible 
together near the eastern limb of the planet. In the case of the 
fourth satellite, a certain regularity in its changes of brightness sug- 
gests that it probably follows the example of our moon in always 
keeping the same face towards the planet. Prof. W. Pickering 
reports that they show certain curious and regularly recurring 
changes of form, which indicate that they are not solid masses, but 
whirling clouds or swarms of minute particles ; his observations, 
however, have not yet received satisfactory confirmation. 

The fifth satellite is at a distance of about 112,500 miles, and its 
period of revolution is ll h 57 m 22. s 6. Its diameter is probably less 
than 100 miles. 

273. Eclipses and Transits. — The orbits of the satellites are 
so nearly in the plane of the planet's orbit that with the ex- 
ception of the fourth, which sometimes escapes, they are 
eclipsed at every revolution. When the planet is either at 
opposition or conjunction, the shadow, of course, is directly 
behind it, and we cannot see the eclipse at all. At other times 
we ordinarily see only the beginning or the end ; but when the 
planet is very near quadrature the shadow projects so far to 
one side that the whole eclipse of every satellite, except the 
first, takes place clear of the disc, and both the disappearance 
and reappearance can be seen. 

Two important uses have been made of these eclipses : they 
have been employed for the determination of longitude, and 



§ 274] SATURN. 201 

they furnish the means of ascertaining the time required by light 
to traverse the space between the earth and the sun. (See Appen- 
dix, Arts. 431-434.) 



SATURN. 

274. This is the most remote of the planets known to the 
ancients. It appears as a star of the first magnitude (out- 
shining all of them, indeed, except Sirius), with a steady, 
yellowish light, not varying much in appearance from month 
to month, though in the course of 15 years it alternately gains 
and loses nearly 50 per cent of its- brightness with the chang- 
ing phases of its rings ; for it is unique among the heavenly 
bodies, a great globe attended by eight satellites and sur- 
rounded by a system of rings, which has no counterpart else- 
where in the universe so far as known. 

Its mean distance from the sun is about 9|- astronomical 
units, or 886,000000 miles ; but the distance varies over 
100,000000 miles on account of the considerable eccentricity of 
the orbit (0.056). Its least distance from the earth is about 
774,000000 miles, the greatest, about 1028,000000. The incli- 
nation of the orbit to the ecliptic is 2|°. The sidereal period 
is about 29^ years, the synodic period being 378 days, or a year 
and a fortnight nearly. 

275. Dimensions, Mass, etc. — The apparent mean diameter 
of the planet varies according to the distance from 14" to 20". 
The planet is more flattened at the poles than any other 
(nearly -j^), so that while the equatorial diameter is about 
75,000 miles, the polar is only 68,000 : the mean diameter 
(Art. 112) being not quite 73,000/ — a little more than nine 
times that of the earth. Its surface is about 84 times that of 
the earth, and its volume 770 times. Its mass is found (by 

1 Barnard's recent measures give a diameter about 1000 miles larger. 



202 



SATURN. 



a- 




Fig. 56. — Saturn and his Rings. 



§ 275 J SURFACE, ALBEDO, SPECTRUM. 203 

means of its satellites) to be 95 times that of the earth, so 
that its mean density comes out only one-eighth that of the 
earth, — actually less than that of water ! It is by far the least 
dense of all the planetary family. 

Its mean superficial gravity is about 1.2 times as great as 
gravity upon the earth, varying, however, nearly 25 per cent 
between the equator and the pole, so that at the planet's 
equator it is practically the same as upon the earth. It 
rotates on its axis in about 10 hours, 14 minutes, but different 
spots give various results, as in the case of Jupiter. 

The equator of the planet is inclined about 27° to the plane 
of its orbit — about 28° to the ecliptic. 

276. Surface, Albedo, Spectrum. — The disc of the planet, 
like that of Jupiter, is shaded at the edge, and like Jupiter it 
shows a number of belts arranged parallel to the equator. 
The equatorial belt is very bright, and is often of a delicate 
pinkish tinge. The belts in higher latitudes' are comparatively 
faint and narrow, while just at the pole there is usually a cap 
of olive green (see Fig. 56). 

Zollner makes the mean albedo of the planet 0.52, about the 
same as that of Venus. 

The planet's spectrum is substantially like that of Jupiter, 
but the dark bands are more pronounced. These bands, how- 
ever, do not appear in the spectrum of the ring, which prob- 
ably has very little atmosphere. As to its physical condition 
and constitution, the planet is probably much like Jupiter, 
though it does not seem to be " boiling " quite so vigorously. 

277. The Rings. — The most remarkable peculiarity of the 
planet is its ring system. The globe is surrounded by three 
thin, flat, concentric rings, like circular discs of paper pierced 
through the centre. They are generally referred to as A. B, 
and C, A being the exterior one. 



204 Saturn's rings. [§ 277 

Galileo half discovered them in 1610; 1.0., he saw with bis little 
telescope two appendages, one on each side of the planet; but ho could 

make nothing of them, and after a while he Lost them. The problem 
remained unsolved for nearly fifty years, until Iluyobens explained 
the mystery in 1(555. Twenty years Later I). Cassini discovered that 
the ring is double; i.e., composed of two concentric rings, with a dark 

line of separation between them; and in 1850, Bond of Cambridge, 

[J.S., discovered the third "dusky" or "gauze" ring between the 
principal ring and the planet, (It was discovered a fortnight later, 

independently, by Pawes, in England.) 

The outer ring, /f, has a diameter of about 170,000 miles, 

and a width of about 1 1,000. Cassini's division is about 2000 
miles wide ; the ring />, which is much the broadest of the 




Km. f>7. — The Piwi-HOH of Satura'i Rings. 

three, is about 17,000. The semi-transparent ring, (\ has a 
width of about 10,000 miles, leaving a clear space of from 
sooo to 9000 miles in width between the planet's equator and 

its inner edge. The thickness of the rings is extremely small, 
— probably not over 100 miles, as proved by the appearance 

presented, when once in L5 years we view r them edgewise. 

The recent researches of H. Struve show that the mass of 

the rings, and their mean density an 4 , also surprisingly small, 

— so small that the rings exert hardly more influence on 






§ 27? ] SATELLITES. 205 

the motion of the satellites than if they were composed oi 
" immaterial light," to use his own expression. 

278. Phases of the Rings. — The plane of the rings coin- 
cides with the plane of the planet's equator, and is inclined 
about 28° to the ecliptic. It, of course, remains parallel 
to itself at all times. Twice in a revolution of the planet, 
therefore, this plane sweeps across the orbit of the earth (too 
small to be shown in the figure — Fig. 57), occupying nearly a 
year in so doing ; and whenever the plane passes between the 
earth and the sun the dark side of the ring is towards us, and 
the edge alone is visible, as when the planet is at 1 or 2; 
when it is at the intermediate points 3 and 4 the rings present 
their widest opening. 

When the ring is exactly edgewise towards us only the largest tele- 
scopes can see it, like a fine needle of light piercing the planet's ball, 
as in the uppermost engraving of Fig. 56. It becomes obvious at 
such times that the thickness of the rings is not uniform, since con- 
siderable irregularities appear upon the line of light at different 
points. The last period of disappearance was in 1892 ; the next will 
be in 1907. 

279. Structure of the Rings. — It is now universally ad- 
mitted that they are not continuous sheets, either solid or 
liquid, but mere swarms of separate particles, each particle pur- 
suing its own independent orbit around the planet, though all 
moving nearly in a common plane. 

The idea was first suggested by J. Cassini, in 1715, but was lost 
sight of until again brought into notice by Bond, in 1850. A little 
later Pierce proved, from mechanical considerations, that the rings 
could not be solid ; and not long after Maxwell showed that they 
could not be " continuous sheets " of any kind, either solid or liquid, 
but might be composed of separate particles moving independently. 
More recently, Muller and Seeliger have shown from photometric 
observations that the variations in the brightness of the ring corre- 
spond to this "meteoric theory" ; and still more recently (in 1895), 



206 SATELLITES. [§ 280 

Keeler has demonstrated, by a most beautiful and delicate spectro- 
scopic observation, that the outer edge of the ring in its rotation 
really moves more slowly than the inner, just as the theory requires. 
It remains uncertain whether the rings constitute a system that is 
permanently stable, or whether they are liable ultimately to be 
broken up and disappear. 

280. Satellites. — Saturn has eight of these attendants, the 
largest of which was discovered by Huyghens in 1655. It 
looks like a star of the ninth magnitude, and is easily seen 
with a three-inch telescope. The smallest one, the seventh in 
order of distance from the planet, was discovered by Bond, at 
Cambridge (U.S.) in 1848. 

Since the order of discovery does not agree with that of distance, it 
has been found convenient to designate them by the names assigned 
by Sir John Herschel, as follows, beginning with the most remote 
viz. : — 

Iapetus (Hyperion), Titan, Rhea, Dione, Tethys; 

Enceladus, Mimas. 

(The name, Hyperion, was not given by Herschel, but interpolated after its dis- 
covery by Bond.) 

The range of the system is enormous. Iapetus has a distance of 
2,225,000 miles, with a period of 79 days, nearly as long as that of 
Mercury. On the western side of the planet, this satellite is always 
much brighter than upon the eastern, showing that, like our own 
moon, it keeps the same face towards its primary. 

Titan, as its name suggests, is by far the largest. Its distance is 
about 770,000 miles, and its period a little less than 16 days. It is 
probably 3000 or 4000 miles in diameter, and, according to Stone, its 
mass is ¥ g^ of Saturn's, or about double that of our moon. The orbit 
of Iapetus is inclined nearly 10° to the plane of the rings, but all of 
the other satellites move almost exactly in their plane, and all the five 
inner ones in orbits nearly circular. 

URANUS. 

281. Uranus (not U-ra'nus) was the first planet ever "dis- 



§ 281 J SATELLITES OF URANUS. 207 

covered," and the discovery created great excitement and 
brought the highest honors to the astronomer. It was found 
accidentally by the elder Herschel on March 13, 1781, while 
"sweeping" for interesting objects with a seven-inch reflector 
of his own construction., He recognized it at once by its disc 
as something different from a star, but supposed it to be a 
peculiar sort of a comet, and its planetary character was not 
demonstrated until nearly a year had passed. It is easily 
visible to a good eye as a star of the sixth magnitude. 

Its mean distance from the sun is about 19 times that of the 
earth, or about 1800,000000 miles, and the eccentricity of its 
orbit is about the same as that of Jupiter's. The inclination 
of the orbit to the ecliptic is very slight — only 46'. The side- 
real period is 84 years, and the synodic, 369^ days. 

In the telescope it shows a greenish disc about 4" in diam- 
eter, which corresponds to a real diameter of about 32,000 
miles. This makes its bulk about 66 times that of the earth. 
The planet's mass is found from its satellites to be about 14.6 
times that of the earth ; its density, therefore, is 0.22 — about 
the same as that of Jupiter and the sun. 

The albedo of the planet, according to Zollner, is very high, 
0.64, — even a little above that of Jupiter. The spectrum 
exhibits intense dark bands in the red, due to some unidenti- 
fied substance in the planet's atmosphere. These bands explain 
the marked greenish tint of the planet's light. The atmos- 
phere is probably dense. 

The disc is obviously oval, with an ellipticity of about y 1 ^. 
There are no clear markings upon it, but there seem to be 
faint traces of something like belts. No spots are visible from 
which to determine the planet's diurnal rotation. 

282. Satellites. — The planet has four satellites, — Ariel, 
Umbriel, Titania, and Oberon, — Ariel being the nearest to the 
planet. 






208 DISCOVERY OF NEPTUNE. [§ 282 

The two brightest, Oberon and Titania, were discovered by Sir 
William Herschel a few years after his discovery of the planet; 
Ariel and Umbriel, by Lassell, in 1851. 

They are among the smallest bodies in the solar system, and 
the most difficult to see. 

Their orbits are sensibly circular, and all lie in one plane, 
which ought to be, and probably is, coincident with the plane 
of the planet's equator. 

They are very close packed also, Oberon having a distance of only 
375,000 miles, and a period of 13 days, 11 hours, while Ariel has a 
period of 2 days, 12 hours, at a distance of 120,000 miles. Titania, 
the largest and brightest of them, has a distance of 280,000 miles, 
somewhat greater than that of the moon from the earth, with a period 
of 8 days, 17 hours. 

The most remarkable thing about this system remains to be 
mentioned. The plane of their orbits is inclined 82°.2, or 
almost perpendicularly, to f the plane of the ecliptic ; and in 
that plane they revolve backwards. 



NEPTUNE. 

283. Discovery. — The discovery of this planet is reckoned 
the greatest triumph of mathematical astronomy. Uranus 
failed to move precisely in the path computed for it, and was 
misguided by some unknown influence to an extent which 
could almost be seen with the naked eye. The difference 
between the actual and computed places in 1845 was the " in- 
tolerable quantity " of nearly two minutes of arc. 

This is a little more than half the distance between the two prin-. 
cipal components of the double-double star, Epsilon Lyne, the north- 
ern one of the two little stars which form the small equilateral triangle 
with Vega (Arts. 67 and 375). A very sharp eye detects the duplicity 
of Epsilon without the aid of a telescope. 



§ 288] THE PLANET AND ITS ORBIT. 209 

One might think that such a minute discrepancy between 
observation and theory was hardly worth minding, and that 
to consider it " intolerable " was putting the case very strongly. 
But just these minute discrepancies supplied the data which 
were found sufficient for calculating the position of a great 
unknown world, and bringing it to light. As the result of a 
most skilful and laborious investigation, Leverrier (born 1811, 
died 1877) wrote to Galle in substance : — 

i 
" Direct your telescope to a point on the ecliptic in the constellation of 
Aquarius, in longitude 326°, and you will find within a degree of that 
place a new planet, looking like a star of about the ninth magnitude, and 
having a perceptible disc." 

The planet was found at Berlin on the night of Sept. 23, 
1846, in exact accordance with this prediction, within half an 
hour after the astronomers began looking for it, and within 
52' of the precise point that Leverrier had indicated. 

We cannot here take the space for a historical statement, further 
than to say that the English Adams fairly divides with Leverrier the 
credit for the mathematical discovery of the planet, having solved the 
problem and deduced the planet's approximate place even earlier 
than his competitor. The planet was being searched for in England 
at the time it was found in Germany. In fact, it had already been 
observed, and the discovery would necessarily have followed in a few 
weeks, upon the reduction of the observations. 

284. Error of the Computed Orbit — Both Adams and Lever- 
rier, besides calculating the planet's position in the sky, had deduced 
elements of its orbit and a value for its mass, which turned out to be 
seriously wrong, and certain high authorities have therefore character- 
ized the discovery as a " happy accident." This is not so, however. 
While the data and methods employed were not sufficient to deter- 
mine the planet's orbit with accuracy, they were adequate to ascertain 
the planet's direction from the earth. The computers informed the 
observers where to point their telescopes ^and this was all that was neces- 
sary for finding the planet. 



210 neptune's satellite. [§ 285 

285. The Planet and its Orbit. — The planet's mean distance 

from the sun is a little more than 2800,000000 miles (800,- 
000000 miles nearer the sun than it should be according to 
Bode's Law). The orbit is very nearly circular, its eccentricity 
being only 0.009. The inclination of the orbit is about 1|°. 
The period of the planet is about 164 years (instead of 217, as 
as it should have been according to Leverrier's computed 
orbit), and the orbital velocity is about 3\ miles per second. 

Neptune appears in the telescope as a small star of between 
the eighth and ninth magnitudes, absolutely invisible to the 
naked eye, though easily seen with a good opera-glass. Like 
Uranus, it shows a greenish disc, having an apparent diameter 
of about 2".6. The real diameter of the planet is about 35,000 x 
miles, and the volume a little more than 90 times that of the 
earth. 

Its mass, as determined by means of its satellite, is about 
18 times that of the earth, and its density 0.20. 

The planet's albedo, according to Zollner, is 0.46, a trifle 
less than that of Saturn and Venus. 

There* are no visible markings upon its surface, and nothing 
certain is known as to its rotation. 

The spectrum of the planet appears to be like that of 
Uranus, but of course is rather faint. 

It will be noticed that Uranus and Neptune form a " pair of twins," 
very much as the earth and Venus do, being almost alike in magni- 
tude, density, and many other characteristics. 

286. Satellite. — Neptune has one satellite, discovered by 
Lassell within a month after the discovery of the planet 
itself. Its distance is about 223,000 miles, and its period 
5 d 21 h . Its orbit is inclined to the ecliptic at an angle of 34° 
48 f , and it moves backward in it from east to west, like the 
satellites of Uranus. From* its brightness, as compared with 
that of Neptune itself, its diameter is estimated as about the 
same as that of our own moon. 

1 33,000 according to Barnard. 



§ 287] ULTRA-NEPTUNIAN PLANETS, ETC. 211 

287. The Solar System as seen from Neptune. — At Nep- 
tune's distance the sun itself has an apparent diameter of 
only a little more than one minute of arc, — about the diam- 
eter of Venus when nearest us ; and too small to be seen as a 
disc by the naked eye, if there are eyes on Neptune. The 
solar light and heat are there only g-J-g- of what we get at the 
earth. 

Still, we must not imagine that the Neptunian sunlight is 
feeble as compared with starlight, or even moonlight. Even 
at the distance of Neptune the sun gives a light nearly equal 
to 700 full moons. This is about 80 times the light of a 
standard candle at one metre's distance, and is abundant for 
all visual purposes. In fact, as seen from Neptune, the sun 
would look very like a large electric arc lamp, at a distance of 
a few yards. 

288. Ultra-Neptunian Planets. — Perhaps the breaking down of 
Bode's Law at Neptune may be regarded as an indication that the 
solar system terminates there, and that there is no remoter planet ; 
but of course it does not make it certain. If such a planet exists, it 
is sure to be found sooner or later, either by means of the disturbances 
it produces in the motion of Uranus and Neptune, or else by the 
methods of the asteroid hunters, although its slow motion will render 
its discovery in that way difficult. Quite possibly such a discovery 
may come within a few years as a result of the photographic star- 
charting operations now in progress. 

288*. Stability of the Solar System. — It is an interesting and 
important question, once long and warmly discussed, whether the so- 
called " perturbations " which result from the mutual attractions of 
the planets can ever seriously derange the system. It is now nearly 
a century since Laplace and Lagrange first demonstrated that they 
cannot. The system is stable in itself, all the planetary disturbances 
due to gravitation being either of such a character, or so limited in 
extent, that they can never do any harm. 

It does not follow, however, that because the mutual attractions of 
the planets are thus harmless, there may not be other causes which 



212 STABILITY OF THE SOLAR SYSTEM. [§ 288* 

would act disastrously. Many such are conceivable, — such, for in- 
stance, as the retardation of the speed of the planets which would be 
caused by the presence ot a resisting medium in space, or by the en- 
counter of the system with a sufficiently dense and extended cloud of 
meteors. 

But so far as we can now judge, the ultimate cooling of the sun 
(Art. 193) is likely to extinguish life upon the planets long before the 
mechanical destruction of the system can occur from any such exter- 
nal causes. 



§ 289] I I 'MET-. 213 



CHAPTER X. 

COMETS AND METEORS. 

THE NUMBER, DESIGNATION, AND ORBITS OF COMETS. — 
THEIR CONSTITUENT PARTS AND APPEARANCE. — THEIR 
SPECTRA AND PHYSICAL CONSTITUTION. — THEIR PROB- 
ABLE ORIGIN. — REMARKABLE COMETS. — AEROLITES. 
THEIR FALL AND CHARACTERISTICS. — SHOOTING STARS. 
METEORIC SHOWERS. — CONNECTION BETWEEN COMETS 
AND METEORS. 

289. Comets — their Appearance and If Timber. — The word 
u comet *' (derived from the Greek home) means a -hairy star." 
The appearance is that of a rounded cloud of luminous fog 
with a star shining through it, often accompanied by a long 
fan-shaped train or "tail" of hazy light. They present them- 
selves from time to time in the heavens, mostly when unex- 
pected, move across the constellations in a path longer or 
shorter according to circumstances, and remain visible for some 
weeks or months, until they fade out and vanish in the dis- 
tance. The large ones are magnificent objects, sometimes as 
bright as Venus, and visible by day ; with a head as large as 
the moon, and having a train which extends from the horizon 
to the zenith, and is really long enough to reach from the earth 
to the sun. Such comets are rare, however. The majority are 
faint wisps of light, visible only with the telescope. Pig. 58 
is a representation of Donati's comet of 1858, which was one of 
the finest ever seen- 



214 



COMETS. 



§ 289 




Fig. 58. —Naked-eye View of Donati's Comet, Oct. 4, 1858. (Bond.) 

In ancient times, comets were always regarded with terror, as at 
least presaging evil, if not actively malignant, and the notion still 
survives in certain quarters, though the most careful research goes to 



§ 289] DESIGNATION OF COMETS. 215 

prove that they really do not exert upon the earth the slightest per- 
ceptible influence of any kind. 

Thus far our lists contain about 675, about 400 of which 
were observed before the invention of the telescope, and there- 
fore must have been fairly bright. Of the 275 observed since 
then, only a small proportion have been conspicuous to the 
naked eye, perhaps one in five. The total number that visit 
the solar system must be enormous ; for there is seldom a time 
when one at least is not in sight, and even with the telescope 
we see only the few which come near the earth and are favor- 
ably situated for observation. 

290. Designation of Comets. — A remarkable comet gener- 
ally bears the name of its discoverer or of some one who has 
" acquired its ownership," so to speak, by some important 
research concerning it. Thus we have Halley's, Encke's, and 
Donates comets. The ordinary telescopic comets are desig- 
nated only by the year of discovery with a letter indicating 
the order of discovery in that year, as comet " 1890 a " ; or still 
again, with the year and a Eoman numeral denoting the order 
of perihelion passage, as 1890 I, the latter method being the 
most used. In some cases a comet bears a double name, as 
the Lexell-Brooks comet (1889 V), which was investigated by 
Lexell in 1770, and discovered by Brooks on its recent return in 
1889. 

291. Duration of Visibility and Brightness. — The great 
comet of 1811 was observed for seventeen months, and the 
little comet, known as 1889 I, for more than two years, the 
longest period of visibility on record. On the other hand, 
the whole appearance sometimes lasts only a week or two. The 
average is probably not far from three months. 

As to brightness, comets differ widely. About one in five 
reaches the naked-eye limit, and a very few, say four or five in 



216 THEIR ORBITS. [§ 291 

a century, are bright enough to be seen in the day-time. The 
great comet of 1882 was the last one so visible. 

292. Their Orbits. — A large majority of the comets move 
in orbits that are sensibly parabolas (see Appendix, Arts. 439- 
440). A comet moving in such an orbit approaches the sun 
from an enormous distance, far beyond the limits of the solar 
system, sweeps once around the sun, and goes off, never to 
come back. The parabola does not return into itself and form 
a closed curve, like the circle and ellipse, but recedes to infin- 
ity. Of the 280 orbits that have been computed, more than 
200 appear to be of this kind. About 70 orbits are more or 
less distinctly elliptical, and about half a dozen are perhaps 
hyperbolas (see Appendix, Art. 440) ; but the hyperbolas differ 
so slightly from parabolas that the hyperbolic character is not 
really certain in a single case. 

Comets which have elliptical orbits of course return at reg- 
ular intervals. Of the 70 elliptical orbits, there are about a 
dozen to which computation assigns periods near to or exceed- 
ing 1000 years. These orbits approach parabolas so closely 
that their real character is still rather doubtful. About 55 
comets, however, have orbits which are distinctly and certainly 
elliptical, and 30 have periods of less than one hundred years. 
Fifteen of these 30 have been actually observed at two or 
more returns at perihelion. As to the rest of them, some are 
now due within a few years, and some have probably been lost 
to observation, either like Biela's comet (Art. 312), or by hav- 
ing their orbits transformed by perturbations. 

293. The first comet ascertained to move in an elliptical orbit was 
that known as Halley's, with a period of about seventy-six years, its 
periodicity having been discovered by Halley in 1681. It has since 
been observed in 1759 and 1835, and is expected again about 1911. 
The second of the periodic comets (in the order of discovery) is 
Encke's, with the shortest period known, — only three and one-half 
years. Its periodicity was discovered in 1819, though the comet itself 



§293] COMET GROUPS. 217 

had been observed several times before. Fig. 59 shows the orbits of a 
number of short period comets (it would cause confusion to insert 
more of them), and also a part of the orbit of Halley's comet. These 
comets all have periods ranging from three and one-half to eight years, 
and it will be noticed that they all pass very near to the orbit of 
Jupiter. Moreover, each comet's orbit crosses that of Jupiter near 
one of its nodes, the node being marked by a short cross-line on the 



Fig. 59. — Orbits of Short-period Comets. 

comet's orbit. The fact is very significant, showing that these comets 
at times come very near to Jupiter, and it points to an almost certain 
connection between that planet and these bodies. 

294. Comet Groups. — There are several instances in which a 
number of comets, certainly distinct, chase each other along almost 
exactly the same path, at an interval usually of a few months or years, 
though they sometimes appear simultaneously. The most remarkable 
of these "comet groups " is that composed of the great comets of 1668, 
1843, 1880, 1882, and 1887. It is of course nearly certain that the 
comets of such a " group " have a common origin. 



218 PERIHELION DISTANCE. [§ 295 

295. Perihelion Distance, etc. — Eight of the 280 cometary 
orbits, thus far determined, approach the sun within less than 
6,000000 miles, and four have a perihelion distance exceeding 
200,000000. A single comet (that of 1729) had a perihelion 
distance of more than four i astronomical units/ or 375,000000 
miles. It must have been an enormous one, to be visible at 
all under the circumstances. There may, of course, be any 
number of comets with still greater perihelion distances, 
because as a rule we are only able to see such as come reason- 
ably near the earth, and this is probably only a small percent- 
age of the total number that visit the sun. 

The inclinations of cometary orbits range all the way from 
zero to 90°. As regards the direction of motion, all the ellip- 
tical comets having periods of less than 100 years move direct, 
i.e., from west to east, except Halley's comet and TempePs 
comet of 1886. Other comets show no decided preponderance 
either way. 

296. Parabolic Comets are Visitors. — The fact that the 
orbits of most comets are sensibly parabolic, and that their 
planes have no evident relation to the ecliptic, indicates 
(though it does not absolutely prove) that these bodies do not 
in any proper sense belong to the solar system, but are only 
visitors. Such comets come to us precisely as if they simply 
dropped towards the sun from an enormous distance among 
the stars ; and they leave the system with a velocity which, 
if no force but the sun's attraction acts upon them, will 
carry them away to an infinite distance, or until they encoun- 
ter the attraction of some other sun. Their motions are just 
what might be expected of ponderable masses moving among 
the stars under the law of gravitation. 

A slightly different view is advocated by some high authorities, 
and is perhaps tenable, — that these comets come from a great 
distance indeed, but not from among the stars. It may be that our 
solar system, in its journey through space (Art. 342), is accompanied 



§ 296] THE CAPTURE THEORY. 219 

by outlying clouds of nebulous matter, and that these are the source 
of the comets. It is argued that if this were not the case the number 
of hyperbolic orbits would be much greater, because we should meet so 
many more comets than could overtake us. 

297. Origin of Periodic Comets. — But while the parabolic 
comets are thus probably strangers and visitors, there is a 
question as to the periodic comets, which move in elliptical 
orbits. Are we to regard them as native citizens, or only as 
naturalized foreigners, so to speak ? It is evident that, some- 
how or other, many of them stand in peculiar relations to 
Jupiter, Saturn, and other planets, as already indicated in Art. 
293. All short period comets (those which have periods 
ranging from three to eight years) pass very close to the orbit 
of Jupiter, and are now recognized and spoken of as Jupiter's 
" family of comets " ; more than twenty are known at present. 
Similarly, Saturn is credited with two comets, and Uranus 
with three, one' of them being Tempel's comet, which is closely 
connected with the November meteors, and is due on its next 
return in 1900. Finally, Neptune has a family of six, among 
them Halley's comet, and two others which have returned a 
second time to perihelion since 1880. 

298. The Capture Theory. — The generally accepted theory 
as to the origin of these " comet-families " is one first suggested 
by Laplace nearly 100 years ago, — that the comets which com- 
pose them have been captured by the planet to w r hich they 
stand related. A comet entering the system in a parabolic 
orbit, and passing near a planet, will be disturbed, — either 
accelerated or retarded. If it is accelerated, it is easy to 
prove that the original parabolic orbit will be changed to an 
hyperbola, and the comet will never be seen again, but will 
pass out of the system forever ; but if it is retarded, the orbit 
becomes elliptical, and the comet will return at each successive 
revolution to the place where it was first disturbed. 



220 THE LEXELL-BROOKS COMET. [§ 298 

But this is not the end. After a certain number of revo- 
lutions, the planet and the comet will come together a second 
time at or near the place where they met before. The result 
may then be an acceleration, which will send the comet out 
of the system finally ; but it is an even chance at least, that 
it may be a second retardation, and that the orbit and period 
may thus be further diminished : and this may happen over and 
over again, until the comet's orbit falls so far inside that of the 
planet that there is no further disturbance to speak of. Given 
time enough and comets enough, and the result would inevi- 
tably be such a comet-family as really exists. We may add 
that certain researches of Professor Newton of New Haven 
and others, upon the position and distribution of cometary 
orbits, decidedly favor the idea that these bodies do not 
originate in the solar system, but come to us from interstellar 
space. 

The late R. A. Proctor declined to accept this capture theory, and 
maintained with much vigor and ability the theory that comets and 
meteor-swarms have been ejected from the great planets by eruptions 
of some sort. We cannot take space here to discuss the theory, which 
is really not quite so wild as at first it seems ; but the objections to it 
are serious, and we think fatal. 

299. The Lexell-Brooks Comet — The "capture" theory 
has recently received an interesting illustration in the case 
of a little comet, 1889 V, discovered by Mr. Brooks of Geneva, 
N.Y., in July, 1889. It was soon found to be moving with a 
period of about seven years, in an elliptical orbit which passes 
very near to that of Jupiter. (We remark in passing that 
this comet in August divided into four fragments ; see Art. 
314.) On investigating the orbit more carefully, Dr. S. C. 
Chandler of Cambridge (U.S.) discovered that, in 1886, the 
comet and the planet had been close together for some months, 
and that as a consequence the comet's orbit must have been 
greatly changed, the previous orbit having been a much larger 
one with a probable period of nearly twenty-seven years. 



§ 299] PHYSICAL CONSTITUTION OF COMETS. 221 

Now, in 1770, a famous comet appeared, which is known as 
Lexell's, because Lexell computed its orbit. It was bright, 
and came very near the earth, and, according to Lexell's cal- 
culations, was then moving in an orbit with a period of only five 
and a half years, — the first instance of a short-period comet on 
record ; but it was never seen again. Its failure to reappear, 
in 1776, was easily accounted for by the fact that its orbit did 
not then bring it anywhere near the earth. But it should 
have reappeared in 1781, and for a long time its disappear- 
ance was very mysterious, until Laplace, some years later, 
showed that, in 1779, the comet must have come very close 
to Jupiter, perhaps as near as some of its satellites, and that 
in consequence the attraction of that planet had probably 
sent it into a new orbit, not observable from the earth. 

More recent investigations by Leverrier, some thirty years 
ago, show that while the data are insufficient to determine the 
comet's subsequent orbit with certainty, one of the possible 
orbits would have had a period a little less than twenty-seven 
years. This would bring it back, in 1886, after four revolu- 
tions, to the same place which it had occupied in 1779 ; now 
nine of Jupiter's periods are 106f years, so that he, also, would 
have returned to the same place. 

To make a long story short, Mr. Chandler showed it to be 
extremely probable that Brooks's comet, 1889 V, is identical 
with Lexell's comet of 1770. Jupiter first transformed its 
orbit from a parabola to an ellipse, with a period of five and a 
half years ; then removed it from our sphere of observation ; 
and, again, after a century or more, has brought it back. 
What will happen at the next encounter of the comet with the 
planet it is not yet possible to predict. 

The still more recent calculations of Dr. Poor of Baltimore, 
based in part on later and more accurate observations than 
those available to Chandler, appear, however, to make it 
rather more likely that Brooks's comet is not identical with 
Lexell's, but only a member of the same comet group (Art. 



222 DIMENSIONS OF COMETS. [§ 299 

294). The question will have to await another return of the 
comet for final decision. Dr. Poor finds that the comet in 
1886 passed between Jupiter and the orbit of its first satel- 
lite, within about 200,000 miles of the planet's surface. 

PHYSICAL CONSTITUTION OF COMETS. 

300. Constituent Parts of a Comet. — (a) The essential part 
of a comet, that which is always present and gives the comet 
its name, is the coma, or nebulosity, a hazy cloud of faintly 
luminous transparent matter. 

(6) Next we have the nucleus, which, however, is wanting 
in many comets, and makes its appearance only as the comet 
comes near the sun. It is a bright, more or less star-like 
point near the centre of the comet. In some cases it is double, 
or even multiple. 

(c) The tail or train is a stream of light which commonly 
accompanies a bright comet, and is sometimes present even 
with a telescopic one. As the comet approaches the sun, the 
tail follows it ; but as the comet moves away from the sun, it 
precedes. It is always, speaking broadly, directed away from 
the sun, though its precise form and position are determined 
partly by the comet's motion. It is practically certain that 
it consists of extremely rarefied matter which is thrown off by 
the comet and powerfully repelled by the sun. 

It certainly is not — like the smoke of a locomotive or train of a 
meteor — simply left behind by the comet, because as the comet is 
receding from the sun the tail goes before it, as has been said. 

(d) Jets and Envelopes. — The head of a comet is often 
veined by short jets of light, which appear to be spurted out 
from the nucleus ; and sometimes the nucleus throws off a 
series of concentric envelopes, like hollow shells, one within 
the other. These phenomena, however, are seldom observed 
in telescopic comets. 



§ 301] MASS OF COMETS. 223 

301. Dimensions of Comets. — The volume or bulk of a comet 
is often enormous, almost inconceivably so, if the tail is in- 
cluded in the estimate. The head, as a rule, is from 40,000 to 
50,000 miles in diameter (comets less than 10,000 miles in 
diameter would stand little chance of discovery). Comets 
exceeding 150,000 miles are rather rare, though there are 
several on record. 

The comet of 1811 at one time had a diameter of fully 1,200000 
miles, 40 per cent larger than that of the sun. The head of the comet 
of 1680 was 600,000 miles in diameter, and that of Donati's comet, of 
1858, about 250,000. Holmes' comet (1892) exceeded 800,000. 

The diameter of the head changes continually and capri- 
ciously ; on the whole, while the comet is approaching the 
sun the head usually contracts, expanding again as it recedes. 

No entirely satisfactory explanation is known for this behavior, but 
Sir John Herschel has suggested that the change is merely optical ; 
that near the sun a part of the nebulous matter is evaporated by the 
solar heat and so becomes invisible, condensing and reappearing again 
when the comet gets to cooler regions. 

The nucleus ordinarily has a diameter ranging from 100 miles 
up to 5000 or 6000, or even more. Like the comet's head it 
also varies greatly in diameter, even from day to day, so that it 
is probably not a solid body. Its changes, however, do not 
seem to depend in any regular way upon the comet's distance 
from the sun, but rather upon its activity in throwing off jets 
and envelopes. 

The tail of a comet, as regards simple magnitude, is by 
far the most imposing feature. Its length is seldom less 
than from 5,000000 to 10,000000 miles. It frequently attains 
50,000000, and there are several cases where it has exceeded 
100,000000; while its diameter at the end remote from the 
comet varies from 1,000000 to 15,000000. 

302. Mass of Comets. — While the bulk of comets is thus 
enormous, their masses are apparently insignificant, in no case 



224 DENSITY OF COMETS. [§ 302 

at all comparable with that of our little earth, even. The evi- 
dence on this point, however, is purely negative; it does not 
enable us in any case to say just what the mass really is, but 
only to say how great it is not; i.e., it only proves that a 
comet's mass is less than yq-oVoo °^ tne earth's, 1 — how much 
less we cannot yet find out. The evidence is derived from the 
fact that no sensible perturbations are produced in the motions 
of a planet when a comet comes even very near it, although 
in such a case the comet itself is fairly "sent kiting," thus 
showing that gravitation has its full effect between the two 
bodies. 

Lexell's comet, in 1770, and Biela's comet on several occasions, 
have come so near the earth that the length of the comet's period was 
changed by several weeks, while the year was not altered by so much 
as a single second. It would have been changed by many seconds if 
the comet's mass were as much as xtioVtto that °f the earth. 

303. Density of Comets. — This is, of course, almost incon- 
ceivably small, the mass of comets being so minute and their 
volumes so enormous. If the head of a comet, 50,000 miles in 
diameter, has a mass 10 ^ 00Q that of the earth, its mean density 
must be about ^ -qVo that °^ the a ^ r a ^ the sea-level, — far below 
that of the best air-pump vacuum. As for the tail, the density 
must be almost infinitely lower yet. It is nearer to an " airy 
nothing " than anything else we know of. 

The extremely low density of comets is shown also by their 
transparency. Small stars can be seen through the head of a 
comet 100,000 miles in diameter, even very near its nucleus, 
and with hardly a perceptible diminution of their lustre. 

We must bear in mind, however, that the low mean density of a 
comet does not necessarily imply a low density of its constituent parti- 
cles. A comet may be to a considerable extent composed of small 

1 One one-hundred-thousandth of the earth's mass is about ten times 
the mass of the earth's whole atmosphere, and is equivalent to the mass 
of an iron ball about 150 miles in diameter. 



§ 303] 



THE LIGHT OF COMETS. 



225 



heavy bodies, and still have a low mean density, provided they are far 
enough apart. There is much reason, as we shall see, for supposing 
that such is really the case, — that the comet is largely composed of 
small meteoric stones, carrying with them a certain quantity of envel- 
oping gas. 

Another point should be referred to. Students often find it 
impossible to conceive how such impalpable "dust clouds" 
can move in orbits like solid masses, and with such enormous 
velocities. They forget that in a vacuum a feather falls as 




Fm. 60. — Comet Spectra. 

(For convenience in engraving, the dark lines of the solar spectrum in the lowest strip 
of the figure are represented as bright.) 

swiftly as a stone. Interplanetary space is a vacuum far 
more perfect than anything we can produce by air-pumps, and 
in it the lightest bodies move as freely and swiftly as the 
densest, since there is nothing to resist their motion. If all 
the earth were suddenly annihilated except a single feather, 



226 DONATI'S COMET. [§ 303 

the feather would keep right on and continue the same orbit, 
with unchanged speed. 

304. The Light of Comets. — To some extent their light 
may be mere reflected sunlight; but in the main it is light 
emitted by the comet itself under the stimulus of solar action. 
That the light depends in some way on the sun is shown by 
the fact that its brightness usually varies with its distance 
from the sun, according to the same law as that of a planet. 

But the brightness frequently varies rapidly and capri- 
ciously without any apparent reason ; and that the comet is 




Fig. 61. — Head of Donati's Comet, Oct. 5, 1858. (Bond.) 

self-luminous when near the sun is proved by its spectrum, 
which is not at all like the spectrum of reflected sunlight, but 
is a spectrum of bright bands, three of which are usually seen, 



§ 304] FORMATION OF TAIL. 227 

and have been identified repeatedly and certainly with the 
spectrum of gaseous hydrocarbons. (All the different hydro- 
carbon gases give the same spectrum at the temperature of a 
Bun sen burner.) This spectrum is absolutely identical with 
that given by the blue base of a candle flame, or, better, by 
a Bunsen burner consuming ordinary coal gas. 

Occasionally a fourth band is seen in the violet, and when the 
comet approaches unusually near the sun, the bright lines of sodium, 
and other metals (probably iron), sometimes appear. There seem to 
be cases, also, when different bands replace the ordinary ones, and 
Holmes's comet in 1892 showed a purely continuous spectrum. Fig. 60 
represents the ordinary comet spectrum, compared with the solar spec- 
trum and with that of a candle flame. The spectrum makes it almost 
certain that hydrocarbon gases are present in considerable quantity, 
and that these gases are somehow rendered luminous ; not probably 
by any general heating, however, for there is no reason to think that 
the general temperature of a comet is very high. Nor must we infer 
that the hydrocarbon gas, because it is so conspicuous in the spec- 
trum, necessarily constitutes most of the comet's mass : more likely 
it is only a very small fraction of the whole. 

305. Phenomena that accompany a Comet's Approach to the 
Sun. — When the comet is first discovered, it is usually a mere 
round, hazy cloud of faint nebulosity, a little brighter near the 
middle. As it approaches the sun it brightens rapidly, and 
the nucleus appears. Then on the sunward side the nucleus 
begins to emit luminous jets, or else to throw off more or less 
symmetrical envelopes, which follow each other at intervals of 
some hours, expanding or growing fainter, until they are lost 
in the nebulosity of the head. 

Fig. 61 shows the envelopes as they appeared in the head of 
Donati's cornet of 1858. At one time seven of them were vis- 
ible together : very few comets, however, exhibit this phe- 
nomenon with such symmetry. More frequently the emissions 
from the nucleus take the form of jets and streamers. 



228 



FORMATION OF TAIL. 



[§306 



> ^ To Sun 













■ 

• 

' 1 

'-V- 









Fig. 62. — Formation of a Comet's Tail by 
Matter expelled from the Head. 



306. Formation of Tail.— 

The tail appears to be formed 
of material which is first pro- 
jected from the nucleus of the 
comet towards the sun, and 
then afterwards repelled by 
the sun, as illustrated by Fig. 
62. At least this theory has 
the great advantage over all 
others which have been pro- 
posed that it not only ac- 
counts for the phenomenon 
in a general way, but admits 
of being worked out in detail 
and verified mathematically, by comparing the actual size 
and form of the planet's tail, at different points in the orbit, 
with that indicated by the theory ; and the accordance is 
generally very satisfactory. 

The repelled particles are still subject to the sun's gravita- 
tional attraction, and the effective force acting upon them is 
therefore the difference between the gravitational attraction 
and the electrical (?) repulsion. This difference may or may 
not be in favor of the attraction, but in any case, the sun's 
attracting force is, at least, lessened. The consequence is 
that those repelled particles, as soon as they get a little away 
from the comet, begin to move around the sun in hyperbolic 
orbits (see Art. 439), which lie in the plane of the comet's 
orbit, or nearly so, and are perfectly amenable to calculation. 
In the case of a great comet the tail is usually a sort of 
curved, hollow cone, including the head of the comet at its 
smaller extremity ; in smaller comets the tail is generally a 
comparatively narrow streamer where it issues from the head 



§ 3(K5 ] TYPES OF COMETS' TAILS. 229 

of the comet, brushing out as it recedes, and often showing, 
in photographs, peculiar knots and condensations, which are 
not visible with the telescope. 

The tail is curved because the repelled particles, after leav- 
ing the comet's head, retain their original motion, so that they 
are arranged not along a straight line drawn from the sun to 




Fig. 63. — A Comet's Tail at Different Points in its Orbit near Perihelion. 

the comet, but on a curve convex to the comet's motion, as 
shown in Fig. 63 ; but the stronger the repulsion the less the 
curvature, and the straighter the tail. The nature of the force 
which repels the particles of a comet is, of course, only a 
matter of speculation ; but the idea that it is electrical gener- 
ally prevails, though the detailed explanation is not easy. 
There is no reason to suppose that the matter driven off to 
form the tail is ever recovered by the comet. 

307. Types of Comets' Tails. — Bredichin, of Pulkowa, has 
found that the trains of comets may be classified under three 
different types, as indicated by Fig. 64. 

First, the long, straight rays, composed of matter ^pon which the 
solar repulsion is from ten to fifteen times as great as the attraction 



230 



TYPES OF COMETS TAILS. 



[§ 307 



of gravity, so that the particles leave the comet with a velocity of four 
or five miles a second, which is afterwards increased until it becomes 
enormous. The nearly straight rays, shown in Fig. 58, belong to 

this type. For plausible 
reasons, which, however, 
we cannot stop to explain, 
Bredichin supposes these 
straight rays to be com- 
posed of hydrogen. 

The second type is the 
ordinary, curved, plume- 
like train, like the principal 
tail of Donates comet. In 
trains of this type, sup- 
posed to be due to hydro- 
carbon vapors, the repulsive 
force varies from 2.2 times 
the attraction of gravity for 
particles on the convex edge 
of the tram, to half that 
amount for those on the 
inner edge. The spectrum 
is the same as that of the 
comet's head. 

Third, a few comets show 
tails of still a third type, — 
short, stubby brushes, vio- 
lently curved, and due to 
matter on which the repul- 
sive force is feeble as com- 
pared with gravity. These 
are assigned by Bredichin 
to metallic vapors of con- 
siderable density, with an 
FlG * 64# admixture of sodium, etc. 

Bredichin's Three Types of Cometary Tails. 




308. Unexplained and Anomalous Phenomena. — A curious 
phenomenon, not yet explained, is the dark stripe which, in a 







§ 308] THE NATURE OF COMETS. 231 

large comet approaching the sun, runs down the centre of the 
tail, looking very much as if it were a shadow of the comet's 
head. It is certainly not a shadow, however, because it usually 
makes more or less of an angle 
with the sun's direction. It is 
well shown in Fig. 61. When the 
comet is at a greater distance from 
the sun, this central stripe is usu- 
ally bright, as in Fig. 65 ; and in 
the case of small comets, gener- fig. 65. 

ally all the tail they show is Bright-centred Tail of Coggia's Comet, 

such a narrow streamer. une * 

Not unfrequently, moreover, comets possess anomalous tails,— 
tails directed sometimes. straight toward the sun, and sometimes at 
right angles to that direction. Then sometimes there are luminous 
sheaths, which seem to envelop the head of the comet and project 
towards the sun (Fig. 66), or little clouds of cometary matter which 
leave the main comet like puffs of smoke from a bursting bomb, and 
travel off at an angle until they fade away (see Fig. 66). None of 
these appearances are contradictory to the theory above stated, 
though they are not yet clearly included in it. 

309. The Nature of Comets. — All things considered, the 
most probable hypothesis as to the constitution of a comet, so 
far as we can judge at present, is that its head is a swarm of 
small meteoric particles, widely separated (say pin-heads, many 
yards apart), each carrying with it an envelope of rarefied gas 
and vapor, in which light is produced either by electric dis- 
charges between the solid particles, or by some action due to 
the rays of the sun. As to the size of the constituent par- 
ticles, opinions differ widely. Some maintain that they are 
large rocks : Professor Newton calls a comet a " gravel bank " : 
others say that it is a mere "dust-cloud." The unquestion- 
able close connection between meteors and comets (Art. 327) 
almost compels some " meteoric hypothesis." 



232 DANGER FROM COMETS. [§ 310 

310. Danger from Comets. — In all probability there is none. 
It has been supposed that comets might do us harm in two ways, — 
either by actually striking the earth, or by falling into the sun and 
thus producing such an increase of solar heat as to burn us up. 

As regards the possibility of a collision between a comet and the 
earth, the event is certainly possible. In fact, if the earth lasts long 
enough, it is practically sure to happen, for there are several comet's 
orbits which pass nearer to the earth's orbit than the semi-diameter 
of the comet's head. As to the consequence of such a collision, it is 
impossible to speak with absolute confidence for want of certain knowl- 
edge as to the constitution of a comet. If the solid " particles " of 
which the main portion of the comet is probably composed are no 
larger than pin-heads, the result would be only a fine meteoric 
shower ; if on the other hand they weigh tons, the bombardment 
would be a very serious matter. It is possible too that the mixture 
of the comet's gases with our atmosphere might be a source of danger. 

The encounters, however, will be very rare. If we accept the esti- 
mate of Babinet, they will occur on the average once in about 
15,000000 years. 

If a comet actually strikes the sun, which would necessarily be a 
very rare phenomenon, it is not likely that the least harm will be 
done. The collision might generate about as much heat as the sun 
radiates in eight or nine hours; but the cometary particles would 
pierce the photosphere, and their heat would be liberated mostly below 
the solar surface, simply expanding by some slight amount the diam- 
eter of the sun, but making no particular difference in the amount of 
its radiation for the time being. There might be, and very likely 
would be, a flash of some kind at the solar surface when the shower 
of meteors struck it ; but probably nothing that the astronomer would 
not take delight in observing. 

311. Remarkable Comets. — Our space does not permit us 
to give full accounts of any considerable number. We limit 
ourselves to three, which for various reasons are of special 
interest. 

Biela's comet is, or rather was, a small comet some 40,000 
miles in diameter, at times barely visible to the naked eye, 



§ 311] biela's comet. 283 

and sometimes showing a short tail. It had a period of 6.6 
years, and was the second comet of short period known, hav- 
ing been discovered by Biela, an Austrian officer, in 1826 
(the periodicity of Encke's comet had been discovered seven 
years earlier). Its orbit comes within a few thousand miles 
of the earth's orbit, the distance varying somewhat, of course, 
on account of perturbations ; but the approach is sometimes 
so close that, if the comet and the earth should happen to 
arrive at the same time, there would be a collision. At its 
return, in 1846, it split into two. When first seen on Nov. 28th, 
it was one and single. On Dec. 19th it was distinctly pear- 
shaped, and ten days later it was divided. 

The twin comets travelled along for four months, at an almost 
unchanging distance of about 165,000 miles, without any apparent 
effect upon each other's motions, but both very active from the physical 
point of view, showing remarkable variations and alterations of bright- 
ness entirely unexplained. In August, 1852, the twins were again 
observed, then separated by a distance of about 1,500000 miles; but 
it was impossible to tell which was which. Neither of them has ever 
been seen again, though they must have returned many times, and 
more than once in a very favorable position. 

312. There remains, however, another remarkable chapter 
in the story of this comet. In 1872, on Nov. 27th, just as the 
earth was crossing the track of the lost comet, but some mil- 
lions of miles behind where the comet ought to be, she en- 
countered a wonderful meteoric shower. As Miss Clerke 
expresses it, perhaps a little too positively, " it became evident 
that Biela's comet was shedding over us the pulverized prod- 
ucts of its disintegration." A similar meteoric shower oc- 
curred again in 1885, when the earth once more crossed the 
track of the comet ; and still again in 1892. 

It is not certain whether the meteor swarms thus encountered were 
the remains of the comet itself, or whether they were other small bodies 
merely following in its path. The comet must have been several rail* 



234 THE GREAT COMET OF 1882. [§ 312 

lions of miles ahead of the place where these meteor swarms were 
met, unless it has been set back in its orbit since 1852 by some unex- 
plained and improbable perturbations. But the comet cannot be 
found, and if it still exists and occupies the place it ought to, it must 
have somehow lost the power of shining. 

313. The Great Comet of 1882. — This is the most recent 
of the brilliant comets that have been observed, and will long 
be remembered not only for its magnificent beauty, but for the 
great number of unusual phenomena which it presented. It 
was first seen in the southern hemisphere about Sept. 3d, but 
not in the northern until the 17th, the day on which it arrived 
at perihelion. On that day it was independently discovered 
within 2° or 3° of the sun, near noon, by several observers, who 
had not before heard of its existence. It was visible to the 
naked eye in full sunshine for more than a week after its peri- 
helion passage. It then became a splendid object in the morn- 
ing sky, and continued to be observed for six months. 

That portion of the orbit visible from the earth coincides 
almost exactly with the orbits of four other comets, — those 
of 1668, 1843, 1880, and 1887, with which it forms a " comet 
group/' as already mentioned (Art. 294). The perihelion dis- 
tances of the comets of this group are all less than 750,000 
miles, so that they pass within 300,000 miles of the sun's 
surface ; i.e., right through the corona, and with a velocity 
exceeding 300 miles a second ; and yet this passage through 
the corona does not disturb their motion perceptibly. 

The orbit of the comet of 1882 turns out to be a very elon- 
gated ellipse with a period of about 800 years. The period of 
the comet of 1880 appears to be only seventeen years, while 
the orbits of the other three are sensibly parabolic. 

314. Early in October the comet presented the ordinary 
features. The nucleus was round, a number of well-marked 
envelopes were visible in the head, and the dark stripe down 



§ 314 ] THE "SHEATH." 235 

the centre of the tail was sharply denned. Two weeks later 
the nucleus had been broken up and transformed into a 
crooked stream, some 50,000 miles in length, of five or six 
bright points : the envelopes had vanished from the head, and 
the dark stripe was replaced by a bright central spine. 

At the time of perihelion the comet's spectrum was filled 
with countless bright lines. Those of sodium were easily 
recognizable, and continued visible for weeks ; the other lines 




Fig. 66. — The " Sheath," and the Attendants of the Comet of 1882. 

continued only a few days and were not certainly identified, 
although the general aspect of the spectrum indicated that 
iron, manganese, and calcium were probably present. By the 
middle of October it had become simply the normal comet 
spectrum, with the ordinary hydrocarbon bands. 



236 METEORS AND SHOOTING-STARS. [§ ?14 

The comet was so situated that the tail was directed nearly 
away from the earth, and so was not seen to good advantage, 
never having an apparent length exceeding 35°. The actual 
length, however, at one time was more than 100,000000 miles. 

A unique, and so far unexplained, phenomenon was a faint, 
straight-edged "sheath" of light, which enveloped the por- 
tions of the comet near the head, and projected 3° or 4° in 
front of it, as shown in Fig. 66. Moreover, there were certain 
shreds of cometary matter accompanying the comet, at a dis- 
tance of 3° or 4° when first seen, but gradually receding and 
growing fainter. This also was something new in cometary 
history, though the Lexell-B rooks comet, 1889 V, has since 
shown the same thing. 

Holmes's comet of 1892-3 was in many ways remarkable. When 
first discovered it was already visible to the naked eye, and was 
apparently almost stationary, fast increasing in size as if swiftly 
approaching. For a time a popular impression prevailed that it was 
Biela's lost comet, and might strike the earth, which led to some- 
thing like a " newspaper panic " in certain quarters. It was, how- 
ever, really receding, and never came nearer than 150,000000 miles. 
It was never conspicuous, and had no nucleus or notable train ; but 
its bulk was enormous : at one time its diameter exceeded 800,000 
miles. It experienced many capricious changes of apparent size and 
brightness, and its spectrum was purely continuous, — a thing unpre- 
cedented in comets. It moves in an orbit like that of an asteroid, 
with its perihelion just outside the orbit of Mars, and its aphelion 
close to that of Jupiter, its period being a few days less than seven 
years. 

314 * Photography of Comets. — It is now possible to photo- 
graph comets, and the photographs bring out numerous pecu- 
liarities and details which are not visible to the eye even with 
telescopic aid. This is especially the case in the comet's tail. 
Fig. 66* is from a photograph of Kordame' s comet of 1893, 
for which we are indebted to the kindness of Professor 
Holden, director of the Lick Observatory. As the camera 
was kept pointed at the head of the comet (which was 
moving pretty rapidly) the star-images during the hour's 




COMET RORDAME, JULY 13, 1893. 
Photographed by W. J. Hussey, at the Lick Observatory. 



§ 314*] PHOTOGRAPHY OF COMETS. 237 

exposure are drawn out into parallel streaks, the little irregu- 
larities being due to faults of the clock-work and vibrations 
of the telescope. The knots and streamers which characterize 
the comet's tail were none of them visible in the telescope, 
and are not the same shown upon plates taken the day before 
and the day after. Other plates, made the same evening a 
few hours earlier and later, indicate that the " knots " were 
swiftly receding from the comet's head at a rate exceeding 
150,000 miles an hour. 

In 1892 Barnard discovered a small comet, by the streak it left 
upon one of his star-plates. 

METEORS AND SHOOTING-STARS. 

315. Meteorites. — Occasionally bodies fall upon the earth 
out of the sky. Such a body during its flight through the air 
is called a "Meteorite" or "Bolide/' and the pieces which fall 
to the earth are called "Meteorites," "Aerolites," "Urano- 
liths," or simply "meteoric stones." 

If the fall occurs at night, a ball of fire i'< seen, which moves 
with an apparent velocity depending upon the distance of the 
meteor and the direction of its motion. The fire-ball is gener- 
ally followed by a luminous train, which sometimes remains 
visible for many minutes after the meteor itself has disap- 
peared. The motion is usually somewhat irregular, and here 
and there along its path the meteor throws off sparks and frag- 
ments, and changes its course more or less abruptly. Some- 
times it vanishes by simply fading out in the air, sometimes 
by bursting like a rocket. If the observer is near enough, the 
flight is accompanied by a heavy, continuous roar, emphasized 
now and then by violent detonations. 

The observer must not expect to hear the explosion at the moment 
when he sees it, since sound travels only about twelve miles a minute. 



238 



THE AEROLITES THEMSELVES. 



[§ 315 



If the fall occurs by day, the luminous appearances are 
mainly wanting, though sometimes a white cloud is seen, and 
the train may be visible. In a few cases aerolites have fallen 
almost silently, and without warning. 



316. The Aerolites themselves. — The mass that falls is 
sometimes a single piece, but more usually there are many 
fragments, sometimes numbering thousands ; so that, as the 
old writers say, " it rains stones." The pieces weigh from 500 
pounds to a few grains, 
the aggregate mass 
sometimes amounting 
to a number of tons. 
By far the greater num- 
ber of aerolites are 
stones, but a few, per- 
haps three or four per 
cent of the whole num- 
ber, are masses of near- 
ly pure iron more or 
less alloyed with nickel. 

The total number of 
meteorites which have 
fallen and been gathered 
into cabinets since 1800 
is about 250, — only 10 
of which are iron masses. 
Nearly all, however, con- 
tain a large percentage of 
iron, either in the metal- 
lic form or as sulphide. 
Between 25 and 30 of the 

250 fell within the United States, the most remarkable being those 
of Weston, Conn., in 1807 ; New Concord, Ohio, 1860 ; Amana, Iowa, 
1875; Emmett County, Iowa, 1879 (mainly iron); and Johnson 
County, Ark., 1886 (iron). 




Fig. 67. 
Fragment of one of the Amana Meteoric Stones. 






§ 316] PATH AND MOTION. 239 

Twenty-five of the chemical elements have been found in 
these bodies, including helium (Art. 181) ; but not one new- 
element, though a large number of new minerals appear in 
them, and seem to be characteristic of aerolites. 

The most distinctive external feature of a meteorite is the 
thin, black, varnish-like crust that covers it. It is formed by 
the melting of the surface during the meteor's swift flight 
through the air, and in some cases penetrates the mass in 
cracks and veins. The surface is generally somewhat unevej , 
having " thumb-marks " upon it, — hollows, probably formed 
by the fusion of some of the softer minerals. Fig. 67 is from 
a photograph given in Langley's "New Astronomy," where 
the body is designated, perhaps a little too positively, as " part 
of a comet." 

317. Path and Motion. — When a meteor has been observed 
from a number of different stations, its path can be computed. 
It usually is first seen at an altitude of between 80 and 100 
miles, and disappears at an altitude of between 5 and 10. 
The length of the path may be anywhere from 50 to 500 miles. 
In the earlier part of its course, the velocity ranges from 10 
to 40 miles a second, but this is greatly reduced before the 
meteor disappears. 

In observing these bodies, the object should be to obtain as accurate 
an estimate as possible of the altitude and azimuth of the meteor, at 
moments which can be identified, and also of the time occupied in 
traversing definite portions of the path. The altitude and azimuth 
will enable us to determine the height and position of the meteor, 
while the observations of the time are necessary in computing its 
velocity. By night the stars furnish the best reference points from 
which to determine its position. By day, one must take advantage of 
natural objects or buildings to define the meteor's place, the observer 
marking the precise spot where he stood. By taking the proper 
instrument to the place afterwards, it is then easy to ascertain the 
bearings and altitude. As to the time of flight, it is usual for the 
observer to begin to repeat rapidly some familiar verse of doggerel 



240 LIGHT AND HEAT OF METEORS. [§ 317 

when the meteor is first seen, reiterating it until the meteor disap- 
pears. Then by rehearsing the same before a clock, the number of 
seconds can be pretty accurately determined. 

318. The Light and Heat of Meteors. — These are due 
simply to the destruction of the meteor's velocity by the fric-, 
tion and resistance of the air. When a body moving with a 
high velocity is stopped by the resistance of the air, by far the 
greater part of its energy is transformed into heat. Lord 
Kelvin has demonstrated that the heating effect in the case of 
a body moving through the air with a velocity exceeding ten 
miles a second, is the same as if it were "immersed in a flame 
having a temperature at least as high as the oxyhydrogen 
blow-pipe " ; and, moreover, this temperature is independent 
of the density of the air, — depending only on the velocity of 
the meteor. Where the air is dense, the total quantity of 
heat (i.e., the number of calories developed in a given time) is 
of course greater than where the air is rarified; but the virtual 
temperature of the air itself where it rubs against the surface 
is the same in either case. During the meteor's flight, its sur- 
face, therefore, is raised to a white heat and melted, and the 
liquefied portions are swept off by the rush of air, condensing 
as they cool to form the train. In some cases this train 
remains visible for many minutes, — a fact not easily ex- 
plained. It seems probable that the material must be phos- 
phorescent. 

319. Origin of Meteors. — They cannot be, as some have 
maintained, the immediate product of eruptions from volca- 
noes, either terrestrial or lunar, since they reach our atmo- 
sphere with a velocity which makes it certain that they come 
to us from the depths of space. There is no proof that they 
have originated in any way different from the larger heavenly 
bodies. At the same time many of them resemble each other 
so closely as almost to compel the surmise that these, at least, 



§ 319] SHOOTING-STARS. 241 

had a common source. It is not perhaps impossible that such 
may be fragments which long ago were shot out from now 
extinct lunar volcanoes, with a velocity which made planets 
of them for the time being. If so, they have since been trav- 
elling in independent orbits until they encountered the earth 
at the point where her orbit" crosses theirs. Nor is it impos- 
sible that some of them were thrown out by terrestrial erup- 
tions when the earth was young; or that they have been 
ejected from the planets, or even from the stars. It is only 
certain that during the period immediately preceding their 
arrival upon the earth, they have been travelling in long 
ellipses, or parabolas, around the sun. 



SHOOTING-STARS. 

320. Their Nature and Appearance. — These are the evanes- 
cent, swiftly moving, star-like points of light which may be 
seen every few minutes on any clear moonless night. They 
make no sound, nor has anything been known to reach the 
earth's surface from them. 

For this reason it is probably best to retain, provisionally, at least, 
the old distinction between them and the great meteors from which 
aerolites fall. It is quite possible that the distinction has no real 
ground, — that shooting-stars, as is maintained by many, are just like 
other meteors, except that being so small they are entirely consumed 
in the air ; but then, on the other hand, there are some things which 
rather favor the idea that the two classes differ in about the same way 
as asteroids do from comets. We know that an aerolitic meteor is a 
compact mass of rock. It is possible, or even likely, that a shooting- 
star, on the contrary, is a little dust-cloud, — like a puff of smoke. 

321. Number of Shooting-stars. — Their number is enor- 
mous. A single observer averages from four to eight an hour ; 
but if the observers are sufficiently numerous, and so placed 
as to be sure of noting all that are visible from a given station, 



242 ELEVATION, PATH, AND VELOCITY. [§ 321 

about eight times as many are counted. From this it has 
been estimated that the total number which enter our atmo- 
sphere daily must be between 10,000000 and 20,000000, the 
average distance between them being some 200 miles. 

Besides those which are visible to the naked eye, there is a still 
larger number of meteors which are so small as to be observable only 
with the telescope. 

The average hourly number about 6 o'clock in the morning 
is double the hourly number in the evening ; the reason being 
that in the morning we are in front of the earth, as regards its 
orbital motion, while in the evening we are in the rear. In 
the evening we see only such as overtake us ; in the morning 
we see all that we either meet or overtake. 

322. Elevation, Path, and Velocity. — By observations made 
at stations 30 or 40 miles apart, it is easy to determine these 
data with some accuracy. It is found that on the average the 
shooting-stars appear at a height of about 74 miles, and dis- 
appear at an elevation of about 50 miles, after traversing a 
course 40 or 50 miles long, with a velocity from 10 to 50 miles 
a second, — about 25 on the average. They do not begin to 
be visible at so great a height as the aerolitic meteors ; and 
they are more quickly consumed, and therefore do not pene- 
trate the atmosphere so deeply. 

323. Brightness, Material, and Mass. — Now and then a 
shooting-star rivals Jupiter, or even Venus, in brightness. A 
considerable number are like first-magnitude stars ; but the 
great majority are faint. The bright ones generally leave 
trains. Occasionally it has been possible to get a "snap 
shot," so to speak, at the spectrum of a meteor, and in it the 
bright lines of sodium and magnesium (probably) are fairly 
conspicuous among many others which cannot be identified by 
such a hasty glance. 



§ 323] MATERIAL AND MASS OF SHOOTING-STARS. 243 

Since these bodies are consumed in the air, all that we can 
hope to get of their material is their " ashes." 

In most places its collection and identification is, of course, hope- 
less; but the Swedish naturalist Nordenskiold thought that it might 
be found in the polar snows. In Spitsbergen he therefore melted 
several tons of snow, and on filtering the water he actually detected 
in it a sediment containing minute globules of oxide and sulphide of 
iron. Similar globules have also been found in the products of deep- 
sea dredging. They may be meteoric, but what we now know of the 
distance to which smoke and fine volcanic dust is carried by the wind 
make it not improbable that they may be of purely terrestrial origin. 

We have no way of determining the exact mass of a shoot- 
ing-star^ but from the light it emits as seen from a known dis- 
tance, an approximate estimate can be formed, since we know 
roughly how much energy corresponds to the production of 
a given amount of light. It is likely, on the whole, that an 
ordinary meteor and a good electric incandescent lamp do not 
differ widely in what is called their i luminous efficiency ' ; i.e., 
the percentage of their total energy which is converted into 
visible light. Calculations on this basis indicate that ordinary 
shooting-stars are very minute, weighing only a small fraction 
of an ounce, — from less than a grain up to 50 or 100 grains 
for a very large one. 

324. Meteoric Showers. — There are occasions when these 
bodies, instead of showing themselves here and there in the 
sky at intervals of several minutes, appear in showers of thou- 
sands ; and at such times they do not move at random, but all 
their paths diverge or radiate from a single point in the sky 
known as the radiant; i.e., their paths produced backward all 
pass through this point, though they do not usually start 
there. Meteors which appear near the radiant are apparently 
stationary, or describe paths which are very short, while those 
in the more distant regions of the sky pursue long courses. 
The radiant keeps its place among the stars sensibly un- 



244 



METEORIC SHOWERS. 



[§ 324 



changed during the whole continuance of the shower ; it may 
be for hours and even days, and the shower is named accord- 
ingly from the place of the radiant. Thus we have the 




Fig. 68. — The Meteoric Radiant in Leo, Nov. 13, 1866. 



" Leonids," or meteors whose radiant is the constellation of 
Leo ; the " Andromedes " (or Bielids) ; the " Perseids " ; the 
"Lyrids," etc. 

Fig. 68 represents the tracks of a large number of the Leonids of 
1866, showing the positions of the radiant near Zeta Leonis. 

The radiant is explained as a mere effect of perspective. 
The meteors are all moving in lines nearly parallel with each 
other when encountered by the earth, and the radiant is 
simply the perspective " vanishing-point " of this system of 
parallels. Its position depends entirely on the direction of 
the motion of the meteors with respect to the earth. For 
various reasons, however, the paths of the meteors, after they 



§ 324] DATES OF METEORIC SHOWERS. 245 

enter the air, are not exactly parallel, and in consequence the 
radiant is not a mathematical point, but a " spot " in the sky, 
often covering an area of 3° or 4° square. 

Probably the most remarkable of all the meteoric showers 
that ever occurred was that of the Leonids on Nov. 12th , 
1833. The number of meteors at some stations was estimated 
as high as 100,000 an hour, for five or six hours. " The sky 
was as full of them as it ever is of snow-flakes in a storm." 

325. Dates of Meteoric Showers. — Such meteoric showers 
are caused by the earth's encounter with a swarm of little 
meteors ; and since this swarm pursues a regular orbit around 
the sun, the earth can meet it only when she is at the point 
where her orbit cuts this path. The encounter, therefore, 
must always happen on or near the same day of the year, 
except as in time the meteoric orbits shift their positions on 
account of perturbations. The Leonid showers, therefore, 
always appear on the 13th of November, within a day or two , 
and the Andromedes on the 27th or 28th 1 of the same month. 

In some cases the meteors are distributed along their whole 
orbit, forming a sort of elliptical ring, and are rather widely 
scattered. In that case the shower recurs every year, and 
may continue for several weeks, as is the case with the Per- 
seids, which appear in early August. On the other hand, 
the flock may be concentrated, and then the shower will occur 
only when the earth and the meteor swarm both arrive at the 
orbit-crossing together. This is the case with both the Leo- 
nids and the Andromedes. The showers then occur not every 
year, but only at intervals of several years, though always on 
or near the same day of the month. For the Leonids, the 
interval is about thirty-three years, and for the Bielids about 
thirteen years. 

326. The meteors which belong to the same group have a 
marked family resemblance. The Perseids are yellow, and 

1 In 1892 the shower occurred on Nov. 23d. 



METS A\P METEOV.v [§33 

move with medium velocity. The Leonids are rary s 
meet them/, and they are of a bluish green tint, with vivid 
trains. Fhe Bieli 3s : sluggish ^th^y overtake the ear: 
are reddish, bei^>: less intensely heated than the others, and 
osnally have only ms. During these showers 

no sound is heard, no sensible .-...: nor do 

masses of matter reach the ground : with one exception, how- 
eve: : hat Not. 27th, 1885, /. piece ni meteoric iron fell at 
Mazapil, in Northern Mexico, during the shower of Andronie- 
3, which occurred that evening. The eoinc may be 

: but is certainly interesting Many high author- 
(tic g speak confidently of this e of iron as a pie la's 

comet its this brings as : one of the most important 

astronomical discoveries ;: the last half-centur 

827. The Connection between DcNtets and Meteors. — A: the 
time of the great nirTr sricsh : :> fesscns : ; 

and Twining of New Haven ^vere the first to recognize the 
•.;.: :•:."* .--nd to point out its significance as indicating that 
the meteors must be members of a swarm of bodies revolving 
around the sun in a permanent orbit. In 1S64 Profes- . 
Newton of New Haven, I '^ing up the subject ved 

by an examination of the old records that there had been a 
number of great meteoric sh i s About the middle of Xoveni- 
ber at inte: thirty-three or thirty-] and he 

pre :Vy the repetition of the shower on N 

. or 14th, 1S66. It occurred as predicted, and was or> 
and it was followed by another, in IS " 
which was ... the meteoric swarm being ex- 

90 long a process is to require more than : 
5S :he earth's orbit. The researches of Xewton 
and Adams showed that the flock was moving in a long ellipse 
with a period of thirty -thret 

328. Identification of Meteoric and Cometary Qrbitr — 
Within a few week the shower of 1866 it was found 



828] 



ORBITS OF METEORIC swarms. 



247 



that the orbit pursued by these meteors was identical with 
that of a comet, known as Tempel's, which had been visible 
about a year before; and about the same time Sehiaparelli 

showed that the Pcrseids, or August meteors, move in an orbit 
identical with that of the bright comet of L862. Now a single 
coincidence might be accidental, but hardly two. Five years 
later came the shower of Andromedes, following in the track 
of Biela's comet ; and among the more than a hundred distinct 




Fig. 09. — Orbits of Meteoric Swarms. 

meteor swarms now recognized, Professor Alexander Herschel 
finds five others which are similarly related, each to its special 
comet. It is no longer possible to doubt that there is a real 
and close connection between these comets and their attend- 
ant meteors. Fig. 69 represents four of the orbits of these 
cometo-meteoric bodies. 



329. Nature of the Connection. — This cannot be said to be 
ascertained. In the case of the Leonids and Andromedes, the 



248 



ORIGIN OF THK LEONIDfl. 



[1320 



meteorio Bwarin follows the oomet, but this does not Been to 
be bo in theoaseof the Perseids, whioh soatter along more or 
less abundantly every \ <;i r. The prevailing belief Lb that the 
oomet Itself Is only the thiokest part <>r the meteoric swarm, 
and that the olouds «>i meteors scattered along its path are M»<' 
result of its disintegration ; but this Is by m> means oertain, 

ii Li r.i.iy (o show that If the oomet really Is suoh a swarm, it. must 
at eaoh return to perihelion gradually break up more and more, aud die 
perse Its constituent partioles along Its path, until the compact swann 
in i beoome a diffuse ling. 'I 'he longer the oomet has been moving 




i'kj. TO, Origin o! kfet Ltonldi. 

around the sun, the more uniformly the partioles will be distributed! 
The Perseids, therefore, are supposed to have been In the system for i 
long time, while the Leonids and Andromedos are believed to be com 
paratively newcomers. Leverrier, Indeed, has gone so far as to indioate 
the year 126 ^ >>. as the time at which [Tranus oaptured Tempers 
oomet, and broughl It Into the system, m Illustrated by Fig. 70. But 
the theory thai meteorio swarms are the product of oometary disinte 
gration assumes ih«« premise thai comets enter the system as compact 

Olouds, which, to sav the least, is not vet certain. 






§330 MR. LOCKYER'S METEORITIC HYPOTHESIS, 2 19 

330. Mr. Lockyer'8 Meteoritic HypotheBiH. V V i 1 1 j i 1 1 the la-l 

few years Mr. Lockyer has been enlarging the astronomical impor- 
tance of meteors. The probable meteoric constitution of the zodiacal 
light, as well as of Saturn's rings, and of the comets, lias long been 
recognized; but be goes much farther, and maintains that all the 
heavenly bodies are either meteoric swarms, more or less condensed, 
or the final products of such condensation ; and upon Uiis hypothesis 
he attempts to explain the evolution of the planetary system, the 
phenomena of variable and colored stars, tint various classes of stellar 
spectra, and the forms and structure of the nebulae, — indeed pretty 
much everything in the heavens from the Aurora Borealis to the sun. 
As a " working hypothesis," his theory is unquestionably Important, 

and has attracted much attention, hut it (Joes not hear criticism in all 
Its details. 



250 THE STARS. 



[§331 



CHAPTER XL 

THE STARS. 

THEIR NATURE, NUMBER, AND DESIGNATION. — STAR 
CATALOGUES AND CHARTS. — PROPER MOTIONS AND 
THE MOTION OF THE SUN IN SPACE. — STELLAR PAR- 
ALLAX. — STAR MAGNITUDES. — VARIABLE STARS. — 
STELLAR SPECTRA. 

331. The solar system is surrounded by an immense void 
peopled only by stray meteors. The nearest star, as far as 
our present knowledge goes, is one whose distance is more 
than 200,000 times as great as our distance from the sun, — 
so remote that from it the sun would look no brighter than 
the Pole-star, and no telescope yet constructed would be able 
to show a single one of all the planets. As to the nature of 
the stars, their spectra indicate that they are bodies resem- 
bling our sun, — that is, incandescent, and each shining with 
its own peculiar light. Some are larger and hotter than the 
sun, others smaller and cooler; some, perhaps, large but 
hardly luminous at all. They differ enormously among them- 
selves, not being, as once thought, as much alike as individuals 
of the same race, but differing as widely as animalcules from 
elephants. 

332. Number of Stars. — Those which are visible to the eye, 
though numerous, are by no means countless. If we take a 
limited region, for instance, the bowl of the Dipper, we shall 
find that the number we can see within it is not very large, — 






§332] NUMBER OF STARS. 251 

hardly a dozen. In the whole celestial sphere, the number of 
stars bright enough to be distinctly seen by an average eye is 
only between 6000 and 7000, even in a perfectly clear and 
moonless sky; a little haze or moonlight will cut down the 
number fully one-half. At any one time not more than 2000 
or 2500 are fairly visible, since near the horizon the small stars 
(which are vastly the more numerous) all disappear. The 
total number which could be seen by the ancient astronomers 
well enough to be observable with their instruments is not 
quite 1100. With even the smallest telescope, however, the 
number is enormously increased. A common opera-glass 
brings out at least 100,000, and with a 2\ inch telescope Arge- 
lander made his " Durchmusterung " of the stars north of the 
equator, more than 300,000 in number. The Lick telescope, 
36 inches in diameter, probably makes visible at least 
100,000000. 

333. Constellations. — The stars are grouped in so-called 
" constellations/' many of which are extremely ancient. All 
of those of the zodiac and most of those near the north pole 
antedate history. Their names are, for the most part, drawn 
from the Greek and Roman mythology, many of them being 
connected in some way or other with the Argonautic Expedi- 
tion. In some cases the eye, with the help of a lively imagi- 
nation, can trace in the arrangement of the stars a vague 
resemblance to the object which gives the name to the constel- 
lation; but generally no reason is obvious for either name or 
boundaries. 

We have already, in Chapter II., given a brief description 
of those constellations which are visible in the United States, 
with maps and directions for tracing them. 

334. Designation of the Stars. — In Art. 24 we have already 
indicated the different methods by which the brighter stars 
are designated, — by proper names, position in the constellation, 



252 STAR-CATALOGUES. [§ 334 

or by letters of the Greek and Roman alphabets. But these 
methods do not apply to the telescopic stars, at least to any 
considerable extent. Such stars we identify by their cata- 
logue number ; that is, we refer to them as No. so-and-so in 
some one's star-catalogue. Thus LI., 21,185 is read " Lalande, 
21,185," and means the star that is so numbered in Lalande's 
catalogue. At present not far from 800,000 stars are cata- 
logued, so that, except in the Milky Way, every star visible 
in a three-inch telescope can be found and identified. Of 
course all the bright stars which have names, have letters also, 
and are sure to be found in every catalogue which covers their 
part of the heavens. A conspicuous star, therefore, has usu- 
ally many " aliases," and sometimes great care is necessary to 
avoid mistakes on this account. 

335. Star-catalogues are carefully arranged lists of stars, 
giving their positions (i.e., their right ascensions and declina- 
tions, or latitudes and longitudes) for a given date, and usually 
also indicating their so-called magnitudes of brightness. The 
earliest of these star-catalogues was made about 125 b.c. by 
Hipparchus of Bithynia, the first of the world's great astrono- 
mers, and gives the latitudes and longitudes of 1080 stars. 
This catalogue was republished by Ptolemy 250 years later, 
the longitudes being corrected for precession ; and during the 
Middle Ages several other catalogues were made by Arabic 
astronomers and those that followed them. The modern cata- 
logues are numerous ; some, like Argelander's " Durchmuster- 
ung," give the places of a great number of stars rather roughly, 
merely as a means of ready identification. Others are " cata- 
logues of precision," like the Pulkowa and Greenwich cata- 
logues, which give the places of only a few hundred so-called 
"fundamental" stars, determined as accurately as possible, 
each star by itself. Finally, we have the so-called "zones," 
which give the place of many thousands of stars, determined 
accurately but riot independently ; that is, their positions are 



§ 335] STAR-CHARTS AND STELLAR PHOTOGRAPHY. 253 

determined by reference to tjie fundamental stars in the same 
region of the sky. 

336. Mean and Apparent Places of the Stars. — The mod- 
ern star-catalogue contains the mean right ascension and declination 
of its stars at the beginning of some designated year ; i.e., the place 
the star would occupy if there were no nutation, or aberration (Art. 
126, and Appendix, 435). To set the actual (apparent) right ascen- 
sion and declination of a star ior some given date, which is what we 
always want in practice, the catalogue place must be " reduced " to 
that date ; i.e., it must be corrected for precession, etc. The opera- 
tion is an easy one with modern tables and formulae, but tedious when 
many stars are in question. 

337. Star-charts and Stellar Photography. — For some pur- 
poses, accurate star-charts are even more useful than cata- 
logues. The old-fashioned and laborious way of making such 
charts was by "plotting" the results of zone observations, but 
at present it is being done by means of photography, vastly 
better and more rapidly. A co-operative international cam- 
paign is now in progress, thp object of which is to secure a 
photographic chart of all the stars down to the 14th magni- 
tude. The work is well advanqed, but its completion can hardly 
be expected much before thp end of the century. One of 
the most remarkable things about the photographic method is 
that there appears to be no limit to the faintness of the stars 
that can be photographed with a good instrument. By in- 
creasing the time of exposure, smaller and smaller stars are 
continually reached. With the ordinary plates and exposure- 
times not exceeding twenty minutes, it is now possible to get 
distinct photographs of stare that the eye cannot possibly see 
with the same telescope. 

Fig. 71 represents the photographic telescope (fourteen 
inches diameter, and eleven feet focus, of the Paris observa- 
tory). The other instruments engaged in the star-chart cam- 
paign are substantially like it, though differing more or less 
in minor details. 



254 



STELLAR PHOTOGRAPHY. 



[§ 337 




FlG. 71. — Photographic Telescope of the Paris Observatory. 



§ 337] STAR MOTIONS. 255 

Professor Pickering of Cambridge, U.S., is also planning an inde- 
pendent work of the same kind, with an instrument having a four- 
lens object-glass of twenty-four inches diameter and eleven feet focus. 
It will take much larger plates and require much shorter exposures 
than the Paris instrument, and so will do the work much more 
rapidly. It is intended to map with it first the northern circum- 
polar region, and then to transfer it to the southern hemisphere. 

STAR MOTIONS. 

338. The stars are ordinarily called "fixed," in distinction 
from the planets, or "wanderers," because they keep their 
positions and configurations sensibly unchanged with respect 
to each other for long periods of time. Delicate observations, 
however, demonstrate that the fixity is not absolute, but that 
the stars are really in motion. Moreover, by the spectroscope 
their rate of motion towards or from the earth can in some 
cases be approximately measured. In fact, it appears that the 
velocities of the stars are of the same order as those of the 
planets. The stars are flying through space far more swiftly 
than cannon-balls, and it is only because of their enormous dis- 
tance from us that they appear to change their positions so 
slowly. 

339. Proper Motion. — If we compare a star's position 
(right ascension and declination) as determined to-day^ with 
that observed 100 years ago, it will ahvays be found to have 
changed considerably. The difference is due in the main to 
precession (Art. 125) ; but after allowing for all such merely 
apparent motions of a star, it generally turns out that within a 
century the star has really altered its place more or less with 
reference to others near it, and this real shifting of its place is 
called its " proper motion." Of two stars side by side in the 
same telescopic field of view, the proper motions may be 
directly opposite, while, of course, the apparent motions (due 
to precession, etc.) will be sensibly the same. 



256 VELOCITY OF STAK MOTIONS. [§339 

Even the largest of these proper motions is very small. 
The largest at present known, that of the so-called " run-away 
star," 1830 Groombridge, is only 7" a year. (This star is not 
visible to the naked eye.) About a dozen stars are known to 
have an annual proper motion exceeding 3", and about 150, so 
far as known at present, exceed 1". The proper motions of 
the bright stars average higher than those of the faint, as 
might be expected, since on the average the bright ones are 
probably nearer. For the first-magnitude stars, the average is 
about J" annually; and for the sixth-magnitude stars, the 
smallest visible to the naked eye, it appears to be about -^". 

Motions of this kind were first detected in 1718 by Halley, who 
found that since the time of Hipparchus the star Arcturus had moved 
towards the south nearly a whole degree, and Sirius about half as 
much. 

340. Velocity of Star Motions. — The proper motion of a 
star gives us very little knowledge as to the star's real motion 
in miles per second. The proper motion is derived from the 
comparison of star-catalogues of different dates, and is only 
the value in seconds of arc of that part of its motion which 
is perpendicular to the line of sight. A star moving straight 
towards us or from us has no proper motion at all ; i.e., no 
change of apparent place which can be detected by comparing 
observations of its position. 

We can, however, in some cases fix a minor limit to the 
velocity of a star. We know, for instance, that the distance 
of the star, 1830 Groombridge, is certainly not less than 
2,000000 ' astronomical units,' and, therefore, since its yearly 
path subtends an angle of 7" at the earth, the length of the 
path must at least equal sixty-nine astronomical units a year, 
which corresponds to a velocity of over 200 miles a second. 
The real velocity must be more than this, but how much 
greater we cannot determine until we know how much the 
star's distance exceeds 2,000000 units, and also how fast it is 
moving towards or from us. 



§ 340] MOTION IN THE LINE OF SIGHT. 257 

In many cases a number of stars in the same region of the 
sky have a motion practically identical, making it almost cer- 
tain that they are real neighbors and in some way connected, 
— probably by community of origin. In fact, it seems to be 
the rule rather than the exception that stars which are appar- 
ently near each other are real comrades ; they show, as Miss 
Clerke expresses it, a distinctly " gregarious " tendency. 

341. Motion in the Line of Sight. — Within the last thirty 
years a method 1 has been developed by which any swift 
motion of a star, directly towards or from us, may be detected 
by means of the spectroscope. 

If a star is approaching us, the lines of its spectrum will 
apparently be shifted towards the violet, according to Doppler's 
principle (Art. 179), and vice versa, if it is receding from us. 
Visual observations of this sort, first made by Huggins in 
1868, and since then by many others, have succeeded in dem- 
onstrating the reality of these motions in the line of sight 
and in roughly measuring some of them. Eecently Vogel of 
Potsdam has taken up the investigation photographically, and 
has obtained results that are far more satisfactory than any 
before reached. He photographs the spectrum of the star and 
the spectrum of hydrogen gas, or some other substance whose 
lines appear in the star spectrum, together upon the same 
plate, the light from both being admitted through the same 
slit. If the star is not moving towards or from us, its lines 
will coincide precisely with those of the comparison spectrum ; 
otherwise, they will deviate one way or the other. 

1 It is not, as students sometimes think, by changes in the apparent 
size and brightness of a star. Theoretically, of course, a star which is 
approaching us must grow brighter, but even the nearest star of all, Alpha 
Centauri (Art. 343) is so far away that if it were coming directly towards 
us at the rate of 100 miles a second, it would require more than 8000 years 
to make the journey ; so that in a century its brightness would only 
. change about two per cent, — far too little to be observed. 




258 THE STINTS WAY. [§341 

Fig. 72 is from one of his negatives of the spectrum of Beta Orionis 
(Rigel), in which one of its dark lines is compared with the corre- 
sponding bright lines in the spectrum 
of hydrogen. The dark line of the 
stellar spectrum (bright in the nega- 
tive) is shifted towards the red by an 
amount which indicates that at the Spectrum of Rigel 

time the star was rapidly receding. '„ „ _. , m „ 1 

r J & Fig. 72. — Displacement of Hy Line 

-ci , -i . , , i , • in the Spectrum of B Orionis. 

For the most part, these motions 
of the stars ; so far as ascertained, seem to range between zero 
and fifty miles a second, with still higher speeds in a few 
exceptional cases. 

342. The "Sun's Way." — The proper motions of the stars 
are due partly to their own real motions, but partly also to the 
motion of the sun, which, like the other stars, is travelling 
through space, taking with it its planets. Sir William Her- 
schel was the first to investigate and determine the direction 
of this motion a century ago. The principle involved is this : 
On the whole the stars appear to drift bodily in a direction 
opposite to the sun's real motion. Those in that quarter of 
the sky which we are approaching open out from each other, 
and those in the rear close up behind us. The motions of the 
individual stars lie in all possible directions, but when we 
deal with them by thousands, the individual is lost in the 
general, and the prevailing drift appears. 

About twenty different determinations of the point, towards 
which the sun's motion is directed, have been made by various 
astronomers. There is a reasonable and almost surprising 
accordance of results, and they all show that the sun is mov- 
ing towards a point in the constellation of Hercules, having a 
right ascension of about 267° (17 h 48 m ), and a declination of 
about 32° north. This point is called the " apex of the sun's 
way." As to the velocity of this motion of the sun, it comes 
out as about 0".05 annually, seen from the average distance of 



§342] PARALLAX OF A STAR. 259 

the standard sixth-magnitude star. It is assumed by high 
authorities, on grounds that we cannot stop to discuss, that 
this distance is about 20,000000 astronomical units, which 
would make the sun's velocity about sixteen miles a second, 
as determined from the " proper motions." The spectroscopic 
observations indicate that it is about eleven miles, and this 
result is probably more trustworthy. 

THE PARALLAX AND DISTANCE OF STARS. 

343. When we speak of the " parallax " of the sun, of the 
moon, or of a planet, we always mean the " diurnal" or " geo- 
centric" parallax (Art. 139); i.e., the apparent semi-diameter 
of the earth as seen from the body. In the case of a star, this 
kind of parallax is practically nothing, never reaching ^oio" o" 
of a second of arc. The expression, " parallax of a star," 
always refers, on the contrary, to its " annual" or "helio- 

E 

Star 




Fig. 73. — The Annual Parallax of a Star. 



centric" parallax; i.e., the apparent semi-diameter, not of the 
earth, but of the earth's orbit, as seen from the star. In 
Fig. 73 the angle at the star is its parallax. 

Even this heliocentric parallax, in the case of most stars, is' 
far too small to be detected by our present instruments : it 
never reaches a single second of arc. But in a few instances 
it has been actually measured. Alpha Centauri, which is our 
nearest neighbor, so far as yet known, has a parallax of about 
0".9, according to the earlier observers, or only 0".75, accord- 
ing to the latest authorities. There are but four or five other 
stars at present known which have a parallax more than half 
as great as this. (For the method of determining stellar 
parallax, see Appendix, Arts. 441-443.) 



260 THE LIGHT-YEAR. [§ 344 

344. Unit of Stellar Distance; the Light-year. — The dis- 
tances of the stars are so enormous that even the radius of 
the earth's orbit, the " astronomical unit " hitherto employed, 
is far too small for convenience. It is better, and now usual, 
to take as the unit of stellar distance the so-called light-year; 
i.e., the distance which light travels in a year. This is about 
63,000 times the distance of the earth from the sun. 

This number is found by dividing the number of seconds in a year 
by 499, the number of seconds required by light to make the journey 
from the sun to the earth (Appendix, Art. 432). 

A star with a parallax of 1" is at a distance of 3.26 light- 

years, and in general the distance in light-years equals -—p 

where p' 1 is the parallax of the star expressed in seconds. 

So far as can be judged from the scanty data, it appears 
that few if any stars are nearer than four light-years from the 
solar system; that the naked-eye stars are probably, for the 
most part, within 200 or 300 years ; and that many of the re- 
moter stars must be thousands, or even tens of thousands, of 
light-years away. 

For the parallaxes of a number of stars, see Table V., 
Appendix. 

THE LIGHT OF THE STARS. 

345. Star Magnitudes. — As has already been mentioned 
(Art. 23), Hipparchus and Ptolemy arbitrarily divided the 
stars into six "magnitudes" according to their brightness, 
the stars of the sixth magnitude being those which are barely 
perceptible by an ordinary eye, while the first class comprise 
about twenty of the brightest. After the invention of the 
telescope the same system was extended to the smaller stars, 
though without any special plan, so that the " magnitudes" 
assigned to telescopic stars by different observers are very 
discordant. 



§ 345] SCALE OF STAR MAGNITUDES. 261 

Heis enumerates the stars clearly visible to the naked eye, north of 
the 35th parallel of south declination, as follows : — 

First Magnitude, 14. Fourth Magnitude, 313. 

Second " 48. Fifth " 854. 

Third " 152. Sixth " 2010. 

Total, 3391. 

It will be noticed how rapidly the numbers increase for the smaller 
magnitudes. Nearly the same holds good also for the telescopic stars, 
though below the tenth magnitude the rate of increase falls off. 

346. Light-ratio and "Absolute Scale" of Star Magnitudes. 

— The scale of magnitudes ought to be such that the "light- 
ratio/' or number of times by which the brightness of any 
star exceeds that of a star which is one magnitude smaller, 
should be the same throughout the whole extent of the scale. 
This relation was roughly, but not accurately, observed by the 
older astronomers, and very recently Professor Pickering of 
Cambridge, U. S., and Professor Pritchard of Oxford, England, 
have made photometric measurements of the brightness of all 
the naked-eye stars visible in our latitude, and have re-classified 
them according to the so-called " absolute scale/' which uses 
a light-ratio equal to the fifth root of 100, (2.51) ; i.e., upon 
this scale a star of the third magnitude is just 2.51 times 
brighter than one of the fourth. 

This ratio is based upon an old determination of Sir John Her 
schel's, who found that the average first-magnitude star is just about 
a hundred times as bright as a star of the sixth magnitude, five mag- 
nitudes fainter. 

On this scale, Altair (Alpha Aquilae) and Aldebaran (Alpha 
Tauri) may be taken as standard first-magnitude stars, while 
the Pole-star and the two pointers are very nearly of the stand- 
ard second magnitude. 

Of course, in indicating the brightness of stars with precision, frac- 
tional numbers must be used; that is, we have stars of 2.4 magni- 
tude, etc. 



262 STARLIGHT COMPARED WITH SUNLIGHT. [§ 346 

Stars that are brighter than Aldebaran or Altair have their bright- 
ness denoted by a fraction, or even by a # negative number ; thus the 
absolute magnitude of Vega is 0.2, and of Sirius —1.4. The necessity 
of these negative and fractional magnitudes for bright stars is rather 
unfortunate, but not really of much importance. 

347. Magnitudes and Telescopic Power. — If a good telescope 
just shows a star of a certain magnitude, we must have a telescope 
with its aperture larger in the ratio of 1.58 : 1, in order to show stars 
one magnitude smaller; (1.58= V2.51). A tenfold increase in the 
diameter of an object-glass theoretically carries the power of vision 
just five magnitudes lower. 

It is usually estimated that the 12th magnitude is the limit of vision 
for a 4-inch glass. It would require, therefore, a 40-inch glass to reach 
the 17th magnitude of the absolute scale. 

Our space does not permit any extended discussion of the methods 
by which the brightness of stars is measured, a subject which has of 
late attracted much attention (see General Astronomy, Arts. 823-829). 

348. Starlight compared with Sunlight. — Zollner and 
others have endeavored to determine the amount of light l re- 
ceived by us from certain stars, as compared with the light of 
the sun. According to him, Sirius gives us about -yooirTi"o~ff75'0ir 
as much light as the sun does, and Capella and Vega about 
TTnroirVo o~o~o "o- At this rate, the standard first-magnitude star, 
like Altair, should give us about ginro ^wornr? an( ^ ** w °ul cl 
take, therefore, about nine million million stars of the sixth 
magnitude to equal the sun. These numbers, however, are 
very uncertain. The various determinations for Vega vary 
more than fifty per cent. 

Assuming what is roughly true, that Argelander's magnitudes agree 
with the absolute scale, it appears that the 324,000 stars of his " Durch- 

1 Undoubtedly, the stars send us heat also, and attempts have been 
made to measure it ; but there is no reason for supposing that the propor- 
tion of stellar heat to solar differs much from the proportion of starlight to 
sunlight ; and if so, the heat of a star must be far below the possibility of 
measurement by any apparatus yet at our command. 



. 



§ 348] LIGHT OF CERTAIN STARS. 263 

musterung," all of them north of the celestial equator, give a light 
about equivalent to 240 or 250 first-magnitude stars. How much 
light is given by stars smaller than the 9| magnitude (which was his 
limit) is not certain. It must greatly exceed that given by the larger 
stars. As a rough guess we may estimate that the total starlight of 
both the northern and southern hemispheres is equivalent to about 
3000 stars like Vega, or 1500 at any one time. According to this, the 
starlight on a clear night is about -^ of the light of a full moon, or 
about Tg-uhnnrs that °^ sunlight. More than 95 per cent of it comes 
from stars which are entirely invisible to the naked eye. 

349. Amount of Light emitted by Certain Stars. — When 
we know the distance of a star in astronomical units, it is easy 
to compute the amount of light it really emits as compared 
with that given off by the sun. It is only necessary to mul- 
tiply the light we now get from it (expressed as a fraction of 
sunlight) by the square of the star's distance in astronomical 
units. Thus, the distance of Sirius is about 550,000 units, and 
the light we receive from it is 7000 000000 °^ sunlight. Mul- 
tiplying this fraction by the square of 550,000, we find that 
Sirius is really radiating more than forty times as much light 
as the sun. As for several other stars, whose distance and 
light have been measured, some turn out brighter, and some 
darker than the sun. The range of variation is very wide, 
and in brilliance the sun holds apparently about a medium 
rank among its kindred. 

350. Why the Stars differ in Brightness. — The apparent 
brightness of a star, as seen from the earth, depends both on 
its distance and on the quantity of light it emits, and the 
latter depends on the extent of its luminous surface and upon 
the brightness of that surface. As Bessel long ago suggested, 
"there may be as many dark stars as bright ones." Taken as 
a class, the bright stars undoubtedly average nearer to us than 
the fainter ones, and just as undoubtedly they also average 
larger in diameter and more intensely luminous; but when we 



264 VARIABLE STARS. [§ 350 

compare any particular bright star with another fainter one, 
we can seldom say to which of these different causes it owes 
its superiority. We cannot assert that the faint star is smaller 
or darker or more distant than that particular bright star, 
unless we know something more about it than the simple fact 
that it is fainter. 

351. Dimensions of the Stars. — The stars are so far away 
that their aipparent diameters are- altogether too small to be 
measured by any known form of micrometer. The sun at the 
distance of the nearest star would measure 1 not quite 0".01 
across. Micrometers, therefore, do not help us in the matter, 
and until very recently we were absolutely without any posi- 
tive knowledge as to the real size of a single one of the stars. 
But in 1889, by a spectroscopic method, more fully explained 
in Art. 360, Vogel succeeded in showing that the bright vari- 
able star, Algol (Beta Persei) (Art. 358), must have a diam- 
eter of about 1,160,000 miles, while its invisible companion is 
about 840,000 miles in diameter, or just about the size of 
the sun. 

VARIABLE STARS. 

352. Classes of Variables. — Many stars are found to change 
their brightness more or less, and are known as "variable." 
They may be classed as follows : — 

I. Stars which change their brightness slowly and con- 
tinuously. 
II. Those that fluctuate irregularly. 

III. Temporary stars which blaze out suddenly and then 

disappear. 

IV. Periodic stars of the type of " Omicron Ceti," usually 

having a period of several months. 

1 This does not refer, of course, to the " spurious disc " of the star 
(Appendix, Art. 408), which is many times larger. 



§362] GRADUAL CHANGES. 265 

V. Periodic stars of the type of " Beta Lyrse," usually hav- 
ing short periods. 
VI. Periodic stars of the " Algol " type, in which the period 
is usually short, and the variation is like what might 
be produced if the star were periodically "eclipsed" 
by some intervening object. 

353. Gradual Changes. — The number of stars which are 
certainly known to be gradually changing in brightness is sur- 
prisingly small. On the whole, the stars present not only in 
position, but in brightness also, sensibly the same relations as 
in the catalogues of Hipparchus and Ptolemy. 

There are, however, a few instances in which it can hardly be 
doubted that considerable alteration has occurred even within the last 
two or three centuries. Thus, in 1610 Bayer lettered Castor as Alpha 
Geminorum, while Pollux, which he called Beta Geminorum, is now 
considerably brighter. There are about a dozen other similar cases 
known, and a much larger number is suspected. 

It is commonly believed that a considerable number of stars have 
disappeared since the first catalogues were made, and that many new 
ones have come into existence. While it is unsafe to deny absolutely 
that such things may have happened, it can be said, on the other 
hand, that not a single case of the kind is certainly known. The dis- 
crepancies between the older and newer catalogues are all accounted 
for by some error or other that has already been discovered. 

354. Irregular Fluctuations. — The most conspicuous star 
of the second class is Eta Argtis (not visible in the United 
States). It varies all the way from above the first magnitude 
(in 1843 it stood next to Sirius) down to the seventh magni- 
tude (invisible to the eye), which has been its status ever 
since 1865, though recently it is reported as slightly brighten- 
ing up again. Alpha Orionis, Alpha Herculis, and Alpha 
Cassiopeiae behave in a similar way, except that their varia- 
tion is quite small, never reaching an entire magnitude. 



266 TEMPORARY STARS. [§ .355 

355. Temporary Stars. — There are eleven well-authenti- 
cated instances of stars which have blazed up suddenly, and 
then gradually faded away (see General Astronomy, Arts. 
842-845). The most remarkable of these is that known as 
Tycho's, which appeared in the constellation of Cassiopeia 
(Art. 28) in November, 1572, was for some days as bright as 
Venus at her best, and then gradually faded away, until at 
the end of sixteen months it became invisible. (There were 
no telescopes then.) It is not certain whether it still exists as 
a telescopic star: so far as we can judge it may be either of 
half a dozen which are near the place determined by Tycho. 

There has been a curious and utterly unfounded notion that this 
star was the " Star of Bethlehem " and would reappear to herald the 
second advent. 

A temporary star which appeared in the constellation Corona 
Borealis, in May, 1866, is interesting as having been spectro- 
scopically examined when near its brightest (second magni- 
tude). It then showed the same bright lines of hydrogen 
which are conspicuous in the solar prominences. Before its 
outburst it was an eighth-magnitude star of Argelander's cata- 
logue, and within a few months it returned to its former low 
estate, which it still retains. 

A more recent instance is that of a sixth-magnitude star 
which in August, 1885, suddenly appeared in the midst of the 
great nebula of Andromeda (Art. 377). In a few months it 
totally disappeared, even to the largest telescopes. Still 
more recently (in 1892) a star of the 4-j- magnitude appeared 
in the constellation of Auriga. At first its spectrum was very 
complicated, showing lines both dark and bright, the bright 
lines of Hydrogen and Helium being especially conspicuous. 
The lines were so displaced as to indicate, in the luminous 
gases, velocities of more than 500 miles a second. In April 
the star became invisible, but brightened up again in the 
autumn, and then showed an entirely different spectrum, 
closely resembling that of a nebula (Art. 380). The phe- 



§ 356] 



TYPES OF VARIABLE STARS. 



m 



nomena of this star have called out a great deal of discussion, 
and cannot be considered to have reached a satisfactory 
explanation. 

356. Variables of the "Omicron Ceti" Type. — These ob- 
jects behave almost exactly like a temporary star in remain- 
ing most of the time faint, suddenly blazing out, and then 



A 


o Ceti '\ Period 11 months ± 
(Mira) 1 \ 

l\ 




B 


y" "^- --*"* \ 

s' /3 Lyras. P=12d.?2h. X^ ^ 


C 




B Persei \ l 

H {Algol) \ j P=2d.20h./<8m.55.4s. 

\ ! 



Fig. 74. — Light-curves of Variable Stars. 

gradually fading away, — but they do it periodically. Omicron 
Ceti, or Mira (i.e., "the wonderful") is the type. It was dis- 
covered in 1596, and was the first variable star known. Dur- 
ing most of the time it is of the ninth magnitude, but at 
intervals of about eleven months it runs up to the fourth, 
third, or even second magnitude, and then back again, the 
whole change occupying about 100 days, and the rise being 
much more rapid than the fall. It remains at its maximum 
about a week or ten days. The maximum brightness varies 
very considerably, and its period, while always about eleven 
months, varies to the extent of two or three weeks. The 
spectrum of the star when brightest is very beautiful, show- 



268 EXPLANATION OF VARIABLE STARS. [§ 357 

ing a large number of intensely bright lines, some of which 
are due to hydrogen and helium. Its light-curve is A in Fig. 74. 1 
Nearly half of all the known variables belong to this class, 
and a large proportion of them have periods which do not 
differ very widely from a year. Most of the periods, how- 
ever, are more or less irregular. Some writers include the 
temporary stars in this class, maintaining that the only differ- 
ence is in the length of their period. 

357. Class V. — The variables of Class V. are mostly of 
short period, and are characterized by a continual rising and 
falling of brightness, running through the whole period. 
Sometimes there are two, or even three, maxima before the 
cycle is completed. The light-curve of Beta Lyrae, the type- 
star of this class (period about thirteen days) is B in Fig. 74. 

358. The " Algol" Type. — In the stars of Class VI. the 
variation is precisely the reverse of that in Class IV. The 
star remains bright for most of the time, but apparently suffers 
a periodical eclipse. The periods are mostly very short, — 
only a few days, — and one little star in the constellation of 
Antlia has a period of less than eight hours. 

Algol (Beta Persei) is the type-star. During most of the 
time it is -of the second magnitude, and it loses about live- 
sixths of its light at the time of obscuration. The fall of 
brightness occupies about 4^- hours. The minimum lasts about 
20 minutes, and the recovery of light takes about 3^- hours. 
The period, a little less than three days, is known with great 
precision, to a single second indeed, and is given in connec- 
tion with the light-curve of the star in Fig. 74. At present 
the period seems to be slowly shortening. Between fifteen 
and twenty variables are now known to belong to this class. 

1 The light-curve diagrams are not drawn to scale, and make no pre- 
tensions to exact accuracy. 






§ 359] EXPLANATION OF THE ALGOL TYPE. 269 

359. Explanation of Variable Stars. — No single explana- 
tion will cover the whole ground. As to progressive changes, 
no explanation need be looked for. The wonder rather is that 
as the stars grow old, such changes are not more notable than 
they are. 

As for irregular changes, no sure account can yet be given. 
Where the range of variation is small (as it is in most cases), 
one thinks of spots upon the surface of the star, more or less 
like sun spots ; and if we suppose these spots to be much more 
extensive and numerous than are the sun spots, and also, like 
them, to have a regular period of frequency, and also that the 
star revolves upon its axis, we find in the combination a pos- 
sible explanation of a large proportion of all the variable stars. 

For the temporary stars, we may imagine either great erup- 
tions of glowing matter, like solar prominences on an enor- 
mous scale ; or, with Mr. Lockyer, we may imagine that they, 
and most of the variable stars, are only swarms of meteors, 
rather compact but not yet having reached the condensed 
condition of our own sun. Outbursts of brightness are the 
result of collisions between such swarms. Stars of the Mira 
type, according to this theory, consist of two such swarms, 
the smaller revolving around the larger in a long oval, so that 
once in every revolution it brushes through the outer portions 
of the larger one. But the great irregularity in the periods 
of variables belonging to this class is hard to reconcile with a 
true orbital revolution, which usually keeps time accurately. 

360. Explanation of the Algol Type. — The natural and 
most probable explanation of the behavior of these stars is that 
th© periodical darkening is produced by the interposition of 
some opaque body between us and the star. This eclipse theory 
has lately received a striking confirmation from the spectro- 
scopic work of Vogel, who has found by the method indicated 
in Art. 341 that about seventeen hours before the obscuration, 
Algol is receding from us at the rate of nearly twenty-seven 



270 EXPLANATION OF THE ALGOL TYPE. [§360 

miles a second, while seventeen hours after the minimum it 
approaches us at the same rate. This is just what it ought to 
do, if it had a large, dark companion, and the two were revolv- 
ing around their common centre of gravity in an orbit nearly 
edgewise to the earth. When the dark star is rushing for- 
ward to interpose itself between us and Algol, Algol itself 
must be moving backwards, and vice versa when the dark star 
is receding after the eclipse. VogePs conclusions are, that the 
distance of the dark star from Algol is about 3,250000 miles ; 
that their diameters are respectively about 840,000 and 
1,160000 miles; that their united mass is about two-thirds 
that of the sun ; and their density about one-fifth that of the 
sun, — not much greater than that of cork. Still more 
recently (1892), Mr. Chandler finds evidence from a slight 
alternate shortening and lengthening of the star's period of 
variation, that the pair are probably moving together around 
a third (invisible) star in an orbit about as large as that of 
Uranus, accomplishing the circuit in about 130 years. But 
Tisserand suggests a different explanation. 

361. dumber and Designation of Variables, and their Range 
cf Variation. — Mr. Chandler's catalogue of known variables, 
with its later supplements, includes 343 objects, and there is 
also a considerable number of suspected variables. , . 

About 200 of the 343 are distinctly periodic. The rest of 
them are, some irregular, some temporary, and in respect to 
many we have not yet certain knowledge whether the varia- 
tion is or is not periodic. 

Table IV., Appendix, contains a list of the naked-eye vari- 
ables visible in the United States. 

Such variable stars as had not names of their own before their 
variability was discovered are at present generally indicated by the 
letters 2?, S, T, etc.; i.e., R Sagittarii is the first discovered variable in 
the constellation of Sagittarius, S Sagittarii is the second, etc. 
1 See note on pages 301-2. 



§361] SECCHl's CLASSES OF SPECTKA. 271 

In a considerable number of the earlier discovered variables, 
the range of brightness is from two to eight magnitudes ; 
that is, the maximum brightness exceeds the minimum from 
6 to 1000 times. In the majority, however, the range is much 
less, — only a fraction of a magnitude. 

It is worth noting that a large proportion of the variables, 
especially those of Classes IV. and V., are reddish in their 
color. This is not true of the Algol type. 



STAR SPECTRA. 

362. As early as 1824 Fraunhofer observed the spectra of a 
number of bright stars by looking at them with a small tele- 
scope with a prism in front of the object-glass. In 1864, as 
soon as the spectroscope had taken its place as a recognized 
instrument of research, it was applied to the stars by Huggins 
and Secchi. The former studied very few spectra, but very 
thoroughly, with reference to the identification of the chemi- 
cal elements in certain stars. He found with certainty in 
their spectra the lines of sodium, magnesium, calcium, iron, 
and hydrogen, and more or less doubtfully a number of other 
metals. Secchi, on the other hand, examined great numbers 
of spectra, less in detail, but with reference to a classification 
of the stars from the spectroscopic point of view. 

363. Secchi's Classes of Spectra. — He made four classes, 
as follows : — 

I. Those which have a spectrum characterized by great in- 
tensity of the dark lines of hydrogen, all other lines being 
comparatively feeble or absent. This class comprises more 
than half of all the stars, — nearly all the white or bluish 
stars. Sirius and Vega are its types. 

II. Those which show a spectrum resembling that of the 
sun; i.e., marked with a great number of fine dark lines. 



272 PHOTOGRAPHY OF STELLAR SPECTRA. [§ 363 

Capella (Alpha Aurigae) and Pollux (Beta Geminorum) are 
conspicuous examples. The stars of this class are also numer- 
ous. The first and second classes together comprise fully 
seven-eighths of all the stars whose spectra are known. 

Certain stars, like Procyon and Altair, seem to be intermediate 
between the first and second classes. The line of demarcation is by 
no means sharp. 

III. Stars which show a spectrum characterized by dark 
bands, sharply defined at the upper or more refrangible edge, 
and shading out towards the red. Most of the red stars, and 
a large number of the variable stars, belong to this class. 
Some of them show, also, bright lines in their spectra. 

IV. This class comprises only a few small stars, which, like 
the preceding, show dark bands, but shading in the opposite 
direction. Usually they also show a few bright lines. There 
are not a few anomalous stars that will not fall into any of 
these classes. 

This classification is by no means entirely satisfactory, and various 
modifications have been proposed for it by Vogel, Lockyer, and others. 
On the whole, however, we give it as the best known and simplest, 
and sufficient for most purposes. 

364. Photography of Stellar Spectra. — The observation of 
these spectra by the eye is very tedious and difficult, and pho- 
tography has of late been brought in most effectively. Hug- 
gins, in England, and Henry Draper, in this country, were the 
pioneers, but incomparably the finest results in this line are 
those that have been obtained by Professor E. C. Pickering, of 
Cambridge, in connection with the Draper Memorial Fund. 
Pickering has recurred to the old method of Fraunhofer, using 
a prism, or prisms, in front of the object-glass of his photo- 
graphic telescope, thus forming a "slitless spectroscope." 
The edges of the prism, or prisms, are placed east and west. 
If the clock-work of the instrument followed the star exactly, 



§363] 



THE SLITLESS SPECTROSCOPE. 



273 



the spectrum formed on the sensitive plate would be a mere nar- 
row streak ; but by allowing the clock to gain or lose slightly, 
the image of the star will move to the east or west by a 
very small quantity during the exposure, converting the streak 
into a band. 

The slitless spectroscope has three great advantages : (1) it saves 
all the light which comes from the star, much of which in the usual 
form of the instrument is lost in the jaws of the slit ; (2) by taking 
advantage of the length of a large telescope, it produces a long spec- 
trum with even a single prism ; (3) and most important of all, it 
gives on the same plate, and with a single exposure, the spectra of 
all the many stars (sometimes more than a hundred) whose images 
fall upon the plate. 

On the other hand, the giving up of the slit precludes the usual 
methods of identifying the lines and measuring their displacements, 
by actually confronting them with comparison spectra. For instance, 
it has not yet been found possible to use the slitless spectroscope for 
determining the absolute motions of the stars in the line of sight. 



364.* With the eleven-inch telescope formerly belonging to 
Dr. Draper, and a battery of four enormous prisms placed in 
front of the object-glass, spectra are obtained with an ex- 
posure of thirty minutes, which before enlargement are fully 
three inches long from the F line to the ultra-violet extremity. 



■111111! ' | IT 1 m m 



Fig. 75. — Photographic Spectrum of Vega. 

They easily bear tenfold enlargement, and show many hun- 
dreds of lines in the spectra of the stars which belong to 
Secchi's second class. Fig. 76 is from one of these photo- 
graphs of the spectrum of Vega. The photograph fails to 
show the lower portion of the spectrum, — i.e., the red, yellow, 



274 TWINKLING OF THE STARS. [f:&04 

and green ; but within a year or two the use of isochromatic 
plates has made it possible to deal with these colors also. 

The spectra of all the naked-eye stars in the northern 
hemisphere have already been photographed and catalogued, 
and the work is well advanced in the southern hemisphere 
by parties sent out from Cambridge to South America. Many 
fainter stars have also been included, and the matter is to be 
followed up with the great Bruce telescope mentioned in Art, 
337. 

The admirable spectrograph ic work of Vogel lias been 
already referred to in Art. 341. 

365. Twinkling or Scintillation of the Stars. — This phe- 
nomenon is purely physical, and not in the least astronomical. It 
depends both upon the irregularities of refraction in the air traversed 
by the light on its way to the eye (due to winds and differences of 
temperature), and also on the fact that the star is optically a luminous 
point without apparent size, — a fact which, under the circumstances, 
gives rise to the optical phenomenon known as "interference." Plan- 
ets which have discs measurable with a micrometer do not sensibly 
twinkle. 

The scintillation is of course greatest near the horizon, and on a 
good night it practically disappears at the zenith. When the image 
of a twinkling star is examined with the spectroscope, dark inter- 
ference-ban d» arc seen moving back and forth in its spectrum. 



§ 36 °J DOUBLE STARS. 275 



CHAPTER XII. 

DOUBLE AND MULTIPLE STARS AND CLUSTERS. — NEBULAE. 
— DISTRIBUTION OF STARS AND CONSTITUTION OF THE 
STELLAR UNIVERSE. — COSMOGONY AND THE NEBULAR 
HYPOTHESIS. 

366. Double Stars. — The telescope shows numerous cases 
in which two stars lie so near each other that they can be 
separated only by a high magnifying power. These are 
" double stars," and at present more than 10,000 such couples 
are known. There is also a considerable number of triple 
stars, and a few which are quadruple. Fig. 76 represents a 
few of the best known objects of each class. The apparent 
distances generally range from 30" downwards, very few tele- 
scopes being able to separate stars closer than a quarter of a 
second. In a large proportion of cases (perhaps a third of all) 
the two components are nearly equal in brightness, but in 
many they are very unequal ; in that case (never when they 
are equal) they often present contrasts of color, and when they 
do, the smaller star (for some reason not known) always has a 
tint higher in the spectrum than that of the larger : if the larger 
is reddish or yellow, the small star will be green, blue, or 
purple. 

Gamma Andromedae and Beta Cygni are fine examples of colored 
doubles for a small telescope. 

367. Stars Optically and Physically Double. — Stars may 
be double in two ways, — optically or physically. In the first 
case they are merely approximated in line with each other, as 



276 DOUBLE STARS. C§ 367 

seen from the earth ; in the second case, they are really near 
each other. In the case of stars that are only optically double, 
it usually happens that after some years we can detect their 
mutual independence in the fact that their relative motion is in 




Fi#. 76. —Double and Multiple Stars. 

a straight line and uniform; i.e., one of them drifts by the other 
in a line which is perfectly straight. This is a simple conse- 
quence of the combination of their independent "proper 
motions." If they are physically connected, we find on the 
contrary that the relative motion is in a concave curve; i.e., 
taking either of them as a centre, the other one appears to 
move around it in a curve. 

The doctrine of chances shows what direct observation con- 
firms, that optical pairs must be comparatively rare, and that 
tbe great majority of double stars must be really physically 



§ 367] BINARY STARS. 277 

connected, probably by the same attraction of gravitation 
which controls the solar system. 

368. Binary Stars. — Stars thus physically connected are 
also known as " binary " stars. They revolve in elliptical 
orbits around their common centre of gravity, in periods which 
range from 14 years to 1500 (so far as at present known), 
while the apparent length of the ovals ranges from 40" to 0".5. 
The older Herschel, a little more than a century ago, first dis- 
covered this orbital motion of " binaries " in trying to ascertain 
the parallax of some of the few double stars which were known 
at his time. It was then supposed that they were simply opti- 
cal pairs, and he expected to detect an annual displacement of 
one member of the pair with reference to the other, from 
which he could infer its annual parallax (Art. 343). He 
failed in this, but found instead a true orbital motion. The 
apparent orbit is always an ellipse ; but this apparent orbit is 
the true orbit seen more or less obliquely ; so that the larger 
star is not usually in the focus of the relative orbit pursued by 
the smaller one. If we assume what is probable, though cer- 
tainly not proved as yet, that the orbital motion of the pair is 
under the law of gravitation, we know that the larger star 
must be in the focus of the true relative orbit of the smaller, 
and, moreover, that the latter must describe around it equal 
areas in equal times. By the help of these principles we can 
deduce from the apparent oval the true orbital ellipse ; but 
the calculation is troublesome and delicate. 

369. At present the number of pairs in which this kind of motion 
has been certainly detected exceeds 200, and it is continually increas- 
ing as our study of the double stars goes on. About fifty pairs have 
progressed so far, either having completed an entire revolution or a 
large part of one, that it is possible to determine their orbits with 
some accuracy. 

The case of Sirius is peculiar. Nearly forty years ago it had been 
found from meridian-circle observations to be moving, for no assign- 



278 



SIZE OF THE ORBITS. 



[§ 369 



able reason, in a small orbit, with a period of about fifty years. In 
1862, Clark, the telescope-maker in Cambridge, U.S., found near it a 

minute companion, which 
explains everything ; only 
we have to admit that this 
faint attendant, which does 



1718 im °' 
7 Virginia. 




not give ty ^tt as much 
light as Sirius itself, has a 
mass more than a quarter 
part as great. It seems to 
be one of Bessel's dark 
stars. Fig. 77 represents 

Orbits of Binary Stars. the apparent orbifcs of twQ 

of the best determined double-star systems, Gamma Virginis and Xi 
Ursse Ma j oris. 



£ Ursoe Majoris 



Fig. 77. - 



370. Size and Form of the Orbits. — The dimensions of a 
double-star orbit can easily be obtained if we know its dis- 
tance from us. Fortunately, a number of stars whose parallaxes 
have been ascertained are also binary ; and assuming the best 
available data, we have the results, given in the little table 
which follows, the real semi-major axis of the orbit (in astro- 
ex" 
nomical units) being always equal to the fraction — , in w r hich 

p n 

a" is the angular semi-major axis of the double star orbit in 
seconds of arc, and p n the parallax of the star. 



Name. 


Assumed 
Parallax. 


Angular 
Semi-axis. 


Real 
hemi-axis. 


Period. 


Mass. 

0=1. 


77 Cassiopeiae 

Sirius 

a Geminorum .... 

a Centauri 

70 Ophiuchi 

61 Cygni 


0".44 

0.38 

0.20? 

0.75 

0.16 

0.43 


8".64 
8.58 
5.54 

17.50 
4.79 

15.40? 


19.6 

22.6 

27.7? 

23.3 

29.9 

35.8? 


195.y2 
52.0? 

266 
77.0 
94.5 

450.0? 


0.18 

4.26? 

0.30? 

2.14 

3.0 

0.23? 



§ 37 °] MASSES OF BINARY STARS. 279 

These double-star orbits are evidently comparable in magni- 
tude with the larger orbits of the planetary system, none -of 
those given being smaller than the orbit of Uranus, and none 
twice as large as that of Neptune. In form they are much 
more eccentric than planetary orbits, and Professor See of 
Chicago has shown that this fact can be accounted for as a 
result of " tidal-evolution," operating upon a pair of nebulous 
masses formed by the separation of a parent nebula into two 
portions, which revolve around their common centre. 

371. Masses of Binary Stars. — If we assume that the 
binary stars move under the law of gravitation, then when we 
know the semi-major axis of the orbit and the period of revolu- 
tion, we can easily find the mass of the pair as compared with 
that of the sun ; much more easily, indeed, than we can deter- 
mine the mass of Mercury or the moon, strange as it may 
seem. It is done simply by the following equation, which we 
give without demonstration (see General Astronomy, Arts. 536 
and 878) : — , 

in which (M + m) is the united mass of the two stars, S is the 
mass of the sun, a is the semi-major axis of the orbit of the 
double star in astronomical units, and t its period in years. 
The final column of the preceding table gives the masses of 
the star-pairs, resulting from such data as we now possess ; 
but the reader must bear in mind that the margin of error is 
very considerable, because of the uncertainty of the orbits and 
parallaxes in question. A very slight error in the parallax 
makes a very great error in the resulting mass. 

372. Planetary Systems attending Stars. — It is a natural ques- 
tion whether some of the small companions that we see near large 
stars may not be the " Jupiters " of their planetary systems. We can 
only say as to this that no telescope ever constructed could even come 
near to making visible a planet which bears to its primary any such 
relations of size, distance, and brightness, as Jupiter bears to the sun. 



280 SPECTROSCOPIC BINARIES. [§ 372 

Viewed from our nearest neighbor among the stars, Jupiter would be 
a little star of about the 21st magnitude, not quite 5" distance from 
the sun, which itself would look like a star of the second magnitude. 
To render a star of the 21st magnitude barely visible (apart from all 
the difficulties raised by the nearness of a larger star) would require 
a telescope more than twenty feet in diameter. If any of the stars have 
planetary systems accompanying them, we shall never be likely to see 
them until our telescopes have attained a magnitude and power as yet 
undreamed of. 

373. Spectroscopic Binaries. — One of the most interesting 
of recent astronomical results is the detection by the spectro- 
scope of several pairs of double stars so close that no telescope 
can separate them. In 1889 the bright component of the well- 
known double star Mizar (Zeta Ursse Ma j oris, Fig. 76) was 
found by Pickering to show the dark lines double in the photo- 
graphs of its spectrum, at regular intervals of about fifty-two 
days. The obvious explanation is that this star is composed 
of two, which revolve around their common centre of gravity 
in an orbit which is turned nearly edgewise towards us. (If it 
was exactly edgewise, the star would be variable like Algol.) 

When the stars are at right angles to the line from them to 
us, one of the two will be moving towards us, while the other 
is moving in an opposite direction ; and as a consequence, 
the lines in their spectra will be shifted opposite ways, accord- 
ing to Doppler's principle (Art. 179). Now since the two 
stars are so close that their spectra overlie each other, the 
result will be simply to make the lines in the compound spec- 
trum look double. From the distance apart of the lines, the 
relative velocity of the stars can be found, and from this the 
size of the orbit and the mass of the stars. Thus it appears 
that in the case of Mizar the relative velocity of the two 
components is about 100 miles per second, the period about 
104 days, and the distance between the two stars about the 
same as the diameter of the orbit of Mars ; from which it fol- 
lows that their united mass is about forty times that of the 
sun. 



§ 373] SPECTROSCOPIC BINARIES. 281 

This makes Mizar really a triple star, the larger of the two that are 
seen with a small telescope being the one that is thus spectroscopically 
split. 

374. The lines in the spectrum of Beta Aurigae exhibit the 
same peculiarity, but the doubling occurs once in four days ; 
the velocity being about 150 miles a second, and the diameter 
of the orbit about 8,000000 miles, while the united mass of the 
two stars is about two and a half times that of the sun. 

These observations of Professor Pickering's were made by 
photographing the spectrum with the slitless spectroscope (Art. 
364), and are possible only where the stars which compose the 
binary are both of them reasonably bright. 

With his slit-spectroscope, Vogel (Art. 341), as has already 
been stated (Art. 360), has been able to detect a similar orbital 
motion in Algol, although the companion of the brighter star 
is itself invisible. More recently, in the case of the bright 
star Alpha Virginis (Spica), he has found a result of the same 
kind. At first the photographic observations of the spectrum 
of this star appeared very discordant. Some days they indi- 
cated that the star was moving toivards us quite rapidly, and 
then again from us ; but it is found that everything can be 
explained by the simple supposition that the star is double 
with a small companion, like that of Algol, not bright enough 
to show itself by its light, but heavy enough to make its part- 
ner swing around in an orbit about 6,000000 miles in diameter, 
once in four days, — the orbit not being quite edgewise to the 
earth, so that the dark companion does not eclipse Spica, as 
Algol is eclipsed by its attendant. Eigel (Beta Orionis) also 
shows traces of a similar periodic variation, though the obser- 
vations have not yet- been continued long enough to deter- 
mine its period precisely. The variable stars, Delta Cephei 
and Beta Lyrae, behave in a similar manner, and probably are 
to be added to the list. These orbits, of course, are very 
rnuch smaller than those of most of the telescopic binaries. 



282 



MULTIPLE STARS — CLUSTERS. 



[§37 



375. Multiple Stars (see Fig. 76). — In a considerable 
number of cases we find three or more stars connected in one 
system. Zeta Cancri consists of a close pair revolving in a 
nearly circular orbit, with a period somewhat less than sixty 
years, while a third star revolves in the same direction around 
them, at a much greater distance, and with a period not less 
than 500 years (not yet fully determined). Moreover, this 
third star is subject to a peculiar irregularity in its motion, 
which seems to indicate that it has an invisible companion 
very near the system, the system being really quadruple. 

In Epsilon Lyrae we have a most beautiful quadruple sys- 
tem, composed of two pairs, each binary with a period of over 
200 years. Moreover, since they have a common proper 
motion, it is probable that the two pairs revolve around 
each other in a period which can be reckoned only in thou- 
sands of years. In Theta Orionis, we have a remarkable object, 
in which the six components are not organized in pairs, but 
are at not very unequal distances from each other. 



376. Clusters. — There are in the sky numerous groups of 
stars, containing from a hundred to many thousand members. 
A few of them are resolvable by the naked eye, as, for in- 
stance, the Pleiades (Fig. 78); some, like Prsesepe in Cancer, 
break up under the power of even an opera-glass (Art. 52); 
but most of them require a large telescope to show the sepa- 
rate components. To the naked eye or small telescopes, if 
visible at all, they look like faint clouds of shining haze ; but 
in a great telescope they are among the most magnificent 
objects the heavens afford. The cluster known as "13 Mes- 
sier," not far from the " apex of the sun's way," is perhaps 
the finest. 

The question at once arises whether the stars in such a 
cluster are comparable with our own sun in magnitude, and 
separated from each other by distances like that between the 
sun and Alpha Centauri, or whether they are really small (for 



§376] 



THE PLEIADES. 



283 



stars) and closely packed, — whether the swarm is no more 
distant than the rest of the stars, or far beyond them. 

Forty years ago the prevalent view was. that these clusters 
were stellar universes, galaxies, like the group of stars to 













+ . 


© 












• 
• 






6 

• 

• 


• 
Asterope 


* Taygtta 


• 
• 


• 
• 

< 

• 


• 


....-• 


Maia Ij^yV 


Celwno 

* 


• 








.•/ 


. 




-£. Pleion 


e ... 


• 

-I. *.*.y 




....... 




Atlas 




Alcyone/' 

• 


£* ./ 

Metope 


Electra 


• 


• 




• 
• 




• 


• 






• 




• 








• 

§ 


• 


• 


• 




+ 


• 







Fig. 78. — The Pleiades. 

which it was supposed the sun belongs, — but so inconceivably 
remote that they dwindled to mere shreds of cloud. It is now, 
however, quite certain that the opposite view is correct. The 
star clusters are among our stars, and form a part of our own 
stellar universe. Large and small stars are so associated in 
the same group as to leave no doubt on this point, although 
it has not yet been possible to determine the actual parallax 
and distance of any cluster. 



284 



GREAT NEBULA IN ANDROMEDA. 



[§877 



NEBULAE. 



377. Besides the luminous clouds which, under the tele- 
•cope, break up into separate stars, there are others which no 
telescopic power resolves, and among them some which are 
brighter than many of the clusters. These irresolvable ob- 
jects, which now number 
more than 8000, are u neb- 
ulae." Two or three of 
them are visible to the 
naked eye ; one, the bright- 
est of all, and the one in 
which the temporary star 
of 1885 appeared, is in the 
constellation of Androm- 
eda (see Fig. 79). An- 
other most conspicuous 
and very beautiful nebula 
is that in the sword of 
Orion. 

The larger and brighter 
nebulae are, for the most 
part, irregular in form, 
sending out sprays and 
streams in all directions, 
and containing dark openings and " lanes. " Some of them 
are of enormous volume. The great nebula of Orion (which 
includes within its boundary the multiple star, Theta Ononis) 
covers several square degrees, and photographs show that 
nearly the whole constellation is enveloped in a faint nebu- 
losity, the wisps attaching themselves especially to the 
brighter stars. 

The nebula of Andromeda is not quite so extensive, but is 
rather more regular in its form. 




Fig. 79. — Telescopic View of the Great Nebula 
in Andromeda. 



377] 



ANNULAR NEBULA IN LYRA. 



285 



The smaller nebulae are, for the most part, more or less 
nearly oval, and brighter in the centre. In the so-called 
" nebulous stars," the cen- 
tral nucleus is like a star 
shining through a fog. 
The "planetary nebulae" 
are about circular and 
have nearly a uniform 
brightness throughout, 
while the rare " annular " 
or "ring nebulae" are 
darker in the centre. Fig. 
80 is a representation of 
the finest of these annular 
nebulae, that in the con- 
stellation of Lyra. There 
are a number of nebulae 
which exhibit a remark- 
able spiral structure in 
large telescopes. There 
are several double nebulae, 
and a few that are variable in brightness, though no regular- 
ity has yet been ascertained in their variation. 

The great majority of the 8000 nebulae are extremely faint, 
even in large telescopes, but the few that are reasonably bright 
are very interesting objects. 

378. Drawings and Photographs of Nebulae. — Until very 
lately the correct representation of a nebula was an extremely 
difficult task. More or less elaborate engravings exist of per- 
haps fifty of the more conspicuous of them, but photography 
has now taken possession of the field. The first success in 
this line was by Henry Draper of New York, in 1880, in pho- 
tographing the nebula of Orion. Since his death, in 1882, 
great progress has been made both in Europe and in this 




Fig. 80. — The Annular Nebula in Lyra. 



286 



PHOTOGRAPHS OF NEBUL K. 



[I 



count. rv, and at present the photographs are continually 
bringing out new and before unsuspected features. Fig. 81, 




Fig. 81. — Mr. Roberts's Thotograph of the Nebula of Andromeda. 

for instance, is from a*photograph of the nebula of Androm- 
eda, taken by Mr. Roberts of Liverpool in 1888, and shows 



§378] PHOTOGRAPHS OF NEBULJS. 287 

that the so-called "dark lanes," which hitherto had been seen 
only as straight and wholly mysterious markings (Tig. 79;, 
are really curved ovals, like the divisions in Saturn's rings. 
The photograph brings out clearly a distinct annular structure 
pervading the whole nebula, which as yet has never been 
made out satisfactorily by the eye with any telescope. 

The photographs not only show new features in old nebulae, but 

they reveal numbers of new nebulae invisible to the eye with any tele- 
scope. Thus, in the Pleiades it has been found that almost all the 
larger stars have wisps of nebulosity attached to them, as indicated by 
the dotted lines in Fig. 78; and in a small territory, in and near the 
constellation of Orion, Pickering, with an eight-inch tele-cope, found 
upon his star-plates nearly as large a number of new nebulae as of 
those that were previously known within the same boundary. 

The photographs of nebulae require generally an exposure of from 
one to two hours. The images of all the brighter stars that fall upon 
the plate, are, therefore, always immensely over-exposed, and seriously 
injure the picture from an artistic point of view. 

The photographic brightness of a nebula, to use such an expression, 
IS many times greater than its brightness to the eye, owing to the fact 
that its light consists mainly in rays which belong to the upper or 
blue portion of the spectrum. It has very little red or yellow in it. 
At least, this is so with all the nebulas whose spectra are characterized 
by bright lines. 

379. Changes in Nebulae. — [t cannot be stated with certainty 
that sensible changes have occurred in any of the nebulae since they 
first began to be observed, — the early instruments were so inferior to 
modern ones that the older drawings cannot be trusted; but some of 
the differences between the older and more recent representations make 
it extremely likely that real changes are going on. Probably after a 
reasonable interval of time photography will settle the question. 

380. Spectra of Nebulae. — One of the most important of 
the early achievements of the spectroscope was the proof that 
the light of many nebulae, if not all, proceeds from gl ow- 
ing gas of low density, and not from aggregations of stars. 



288 SPECTRA OF NEBULAE. [§380 

Huggins, in 1864, first made the decisive observation by find- 
ing bright lines in their spectra. Thus far the spectra of all the 
nebulae that show lines at all appear to be substantially the 
same. Four lines are usually easily observed, two of which 
are due to hydrogen ; but the other two, which are brighter 
than the hydrogen lines, are not yet identified. 

At one time the brightest of the four lines was thought to be due 
to nitrogen, and even yet the statement that such is the case is found 
in many books ; but it is now certain that, whatever it may be, nitro- 
gen is not the substance. Very recently Mr. Lockyer has ascribed this 
line to magnesium, in connection with his meteoric hypothesis. But 
recent elaborate observations of Huggins and others show that this 
identification also is probably incorrect. 

Fig. 82 shows the position of the principal lines so far as observed. 
In the brighter nebulae a number of others are also sometimes seen, 
and photographs show many more, between thirty and forty in all ; 




Fig. 82. — Spectrum of the Gaseous Nebulae. 

among them are several of the lines of Helium. Certain stars also 
show the nebular lines in their spectra ; and Mr. Campbell has found 
one or two which show bright hydrogen lines, extending out on each 
side of the star-spectrum in such a way as to indicate an immense 
envelope of the gas surrounding the star itself. Keeler has succeeded 
in measuring the motion of several of the brightest nebulae by the 
displacement of their spectrum-lines. 

381. Not all nebulae show the bright-line spectrum. Those 
which do (about half the whole number) are of a greenish tint, 
at once recognizable in a large telescope. The white nebulae, 
with the nebula of Andromeda, the brightest of all, at their 
head, present only a plain continuous spectrum, unmarked by 



§ 381] DISTANCE AND DISTRIBUTION OF NEBULAE. 289 

lines of any kind. This, however, does not necessarily indicate 
that the luminous matter is not gaseous, for a gas under pres- 
sure gives a continous spectrum, like an incandescent solid or 
liquid. The telescopic evidence as to the non-stellar consti- 
tution of nebulae is the same for all; no nebula resists all 
attempts at resolution (i.e., breaking up into stars) more stub- 
bornly than that of Andromeda. 1 

As to the real constitution of those bodies, we can only 
speculate. The fact that the luminous matter in them is 
mainly gaseous does not at all make it certain that they do 
not also contain dark matter, either liquid or solid. What 
proportion of it there may be, we have at present no means 
of knowing. 

382. Distance and Distribution of Nebulae. — As to the dis- 
tance, we can only say that, like the star clusters, they are 
within the stellar universe and not beyond its boundaries. 
This is clearly shown by the nebulous stars, first pointed out 
and discussed by the older Herschel. We find all gradations, 
from a star with a little faint nebulosity around it, to nebulae 
which show only the faintest spot of light in the centre. It is 
confirmed also by such peculiar associations of the stars and 
nebulae as we find in the Pleiades. Moreover, in certain curi- 
ous luminous masses, known as the "Nubeculae," near the 
south pole, we have stars, star clusters, and nebulae promis- 
cuously intermingling. 

Taking the sky generally, however, the distribution of the 
nebulae is in contrast with that of the stars. The stars, as we 
shall see, crowd together near the Milky Way. The nebulae, 
on the other hand, are most numerous just where the stars are 
fewest, as if the stars had somehow used up the substance of 
which the nebulae are made. 

1 Some years ago it was stated that Lord Kosse's telescope had partially 
resolved the nebula of Andromeda and the nebula of Orion. This turned 
out to be a mistake. 



290 THE MILKY WAY. [§ 383 



THE SIDEREAL HEAVENS. 

383. The Galaxy, or Milky Way. — This is a luminous belt 
of irregular width and outline, which surrounds the heavens 
nearly in a great circle. It is very different in brightness in 
different parts, and is marked here and there by dark bars and 
patches, which at night look like overlying clouds. For about 
a third of its length (between Cygnus and Scorpio) it is 
divided into two roughly parallel streams. The telescope 
shows it. to be made up almost entirely of small stars from 
the eighth magnitude down ; it contains, also, numerous star 
clusters, but very few true nebulae. 

The galaxy intersects the ecliptic at two opposite points not 
far from the solstices, and at an angle of nearly 60°, the north 
" galactic pole " being, according to Herschel, in the constella- 
tion of Coma Berenices. As Herschel remarks, — 

"The ' galactic plane' is to the sidereal universe much what the 
plane of the ecliptic is to the solar system, — a plane of ultimate refer- 
ence, and the ground plan of the stellar system." 

384. Distribution of Stars in the Heavens. — It is obvious 
that the distribution of the stars is not even approximately 
uniform. They gather everywhere into groups and streams ; 
but, besides this, the examination of any of the great star- 
catalogues shows that the average number to a square degree 
increases rapidly and pretty regularly from the galactic pole to 
the galaxy itself, where they are most thickly packed. This 
is best shown by the " star-gauges " of the older Herschel, each 
of which consists merely in an enumeration of the stars visi- 
ble in a single field of view. He made 3400 of these gauges, 
and his son followed up the work at the Cape of Good Hope 
with 2300 more in the south circumpolar regions. From 
these data it appears that near the pole of the galaxy, the 
average number of stars in a single field of view is only 



§ 384] STRUCTURE OF THE STELLAR UNIVERSE. 291 

about 4 ; at 45° from the galaxy, a little over 10 ; while on the 
galactic circle itself it is 122. 

Herschel, starting from the unsound assumption that the stars are 
all of about the same size and brightness and separated by approxi- 
mately equal distances, drew from his observations numerous untenable 
conclusions as to the form and structure of the " galactic cluster " to 
which the sun was supposed to belong, — theories for a time widely 
accepted, and even yet more or less current in popular text-books, 
though in many points certainly incorrect. 

But although the apparent brightness of the stars does not 
depend entirely, or even mainly, upon their distance, it is cer- 
tain that as a class the faint stars are really more remote, as 
well as smaller and darker than the brighter ones. We may, 
therefore, safely draw a few inferences, which, so far as they 
go, in the main agree with those of Herschel. 

385. Structure of the Stellar Universe. — I. The great ma- 
jority of the stars we see are included within a space having, 
roughly, the form of a rather thin, flat disc, like a watch, with 
a diameter eight or ten times as great as its thickness, our 
sun being not very far from its centre. 

II. Within this space the naked-eye stars are distributed 
with some uniformity, but not without a tendency to cluster, 
as shown in the Pleiades. The smaller stars, on the other 
hand, are strongly " gregarious," and are largely gathered into 
groups and streams which have comparatively vacant spaces 
between them. 

III. At right angles to the galactic plane the stars are 
scattered more evenly and thinly than in it, and we find on 
the sides of the disc the comparatively starless region of the 
nebulae. 

IV. As to the Milky Way itself, it is not certain whether 
the stars which compose it form a sort of thin, flat, continu- 
ous sheet, or whether they are arranged in a sort of ring with 



292 DO THE STABS FORM A SYSTEM ? [§ 385 

a comparatively empty space in the middle, where the sun is 
situated, not far from its centre. 

As to the size of the disc-like space which contains most of the 
stars, very little can be said positively. Its diameter must be as great 
as 20,000 or 30,000 light-years, — how much greater it may be we can- 
not even guess ; and as to the " beyond," we are still more ignorant. 
If, however, there are other stellar systems of the same order as our 
own, these systems are neither the nebulae, nor the clusters which the 
telescope reveals, but are far beyond the reach of any instrument at 
present existing. 

386. Do the Stars form a System? — It is probable (though 
not certain) that gravitation operates between the stars, as 
indicated by the motion of the binaries. The stars are cer- 
tainly moving very swiftly in various directions, and the 
question is whether these motions are governed by gravita- 
tion, and are " orbital " in the ordinary sense of the word. 

There has been a very persistent belief that somewhere 
there is an enormous central sun, around which the stars are 
all circulating in the same way as the planets of the solar 
system move about our own sun. This belief has been abun- 
dantly proved to be unfounded. It is now certain that there 
is no such great body dominating the stellar universe. 

387. Maedler's Hypothesis. — Another less improbable doc- 
trine is that there is a general revolution of the mass of stars 
around the centre of gravity of the whole, — a revolution nearly 
in the plane of the Milky Way. Some years ago, Maedler, in 
his speculations, concluded (though without sufficient reason) 
that this centre of gravity of the stellar system was not far 
from Alcyone, the brightest of the Pleiades, and, therefore, 
that this star was in a sense the ' central sun'; and the idea 
is frequently met with in popular writings. It has no basis of 
reason, however, nor is there yet proof or probability of any 
such general revolution. 



§ 388] COSMOGONY. 293 

388. On the whole, the most reasonable- view seems to be 
that the stars are moving much as bees do in a swarm, each 
star mainly under the control of the attraction of its nearest 
neighbors, though influenced more or less, of course, by that 
of the general mass. If so, the paths of the stars are not 
" orbits " in the strict sense ; that is, they are not paths which 
return into themselves, the forces which at any moment act 
upon a given star being so nearly balanced that its motion 
must be sensibly in a straight line for thousands of years at 
a time. 

The solar system is an absolute despotism, the sun supreme. 
Among the stars, on the other hand, there is no central power, 
but the system is a pure democracy, in which the individuals 
are controlled by the influence of their neighbors, and by the 
authority of the whole community to which they themselves 
belong. 

COSMOGONY. 

389. One of the most interesting topics of speculation re- 
lates to the process by which the present state of things has 
come about. In a forest, to use an old comparison of Her- 
scheFs, we see around us trees in all stages of their life-his- 
tory, from the sprouting seedlings to the prostrate and decaying 
trunks of the dead. Is the analogy applicable to the heavens, 
and can we hope by a study of the present condition and 
behavior of the bodies around us to come to an understanding 
of their past history and probable future ? Possibly to some 
extent. But human life is so short that the processes of 
change are hardly perceptible, and our telescopes and spectro- 
scopes reveal but little of the " true inwardness " of things, so 
that speculation is continually baffled, and its results can 
seldom be accepted as secure. Still, some general conclusions 
seem to have been reached, which are likely to be true ; but 
the pupil is warned that they are not to be regarded as estab- 



294 GENESIS OF THE PLANETARY SYSTEM. [§ 389 

lished in any such, sense as the law of gravitation and the 
theory of planetary motion. 

In a general way we may say that the shrinkage of clouds 
of rarefied matter into more compact masses under the force of 
gravitation, the production of heat by this shrinkage, the effect 
of this heat upon the mass itself and upon neighboring bodies. 
— these principles cover nearly all the explanations that can 
thus far be given for the present condition of the heavenly 
bodies. 

390. Genesis of the Planetary System. — Our planetary sys- 
tem is clearly no ^accidental aggregation of bodies. Masses of 
matter coming haphazard to the sun would move (as comets 
actually do move) in orbits which, though necessarily conic 
sections, would have every degree of inclination and eccen- 
tricity. In the planetary system this is not so. Numerous 
relations exist for which gravitation does not at all account, 
and for which the mind demands an explanation. 

We note the following as the principal : — 

1. The orbits of the planets are all nearly circular (i.e., never very 
eccentric). 

2. They are all nearly in one plane (excepting those of some of the 
asteroids). 

3. The revolution of all, without exception, is in the same direction. 

4. There is a curious and regular progression of distances (ex- 
pressed by Bode's Law: which, however, breaks down with Neptune). 

As regards the planets themselves: — 

5. The plane of every planet's rotation nearly coincides with that 
of its orbit (probably excepting Uranus). 

6. The direction of rotation is the same as that of the orbital revo- 
lution (excepting, probably, Uranus and Neptune). 

7. The plane of orbital revolution of the planet's satellites coincides 
nearly with that of the planet's rotation, wherever this has been ascer- 
tained. 

8. The direction of the satellites' revolution also coincides with that 
of the planet's revolution (with the same limitation). 

9. The largest planets rotate most swiftly. 



§ 391] laplace's nebular hypothesis. 295 

391. Now this arrangement is certainly an admirable one 
for a planetary system, and therefore some have argued that 
the Deity constructed the system in that way, perfect from 
the first. But to one who considers the way in which other 
perfect works usually attain their perfection, — their processes 
of growth and development, — this explanation seems improba- 
ble. It appears far more likely that the planetary system was 
formed by growth than that it was built outright. The theory 
which, in its main features, is now generally accepted, as sup- 
plying an intelligible explanation of the facts, is that known 
as the " nebular hypothesis/' In a more or less crude and 
unscientific form, it was first suggested by Swedenborg and 
Kant, and afterwards, about the beginning of the present cen- 
tury, was worked out in mechanical detail by Laplace. On the 
whole, we may say that while, in its main outlines, the theory 
is probably true, it also probably needs serious modifications in 
its details. 

392. Laplace's Nebular Hypothesis. — He maintained (a) 
that at some time in the past 1 the matter which is now 
gathered into the sun and planets was in the form of a 
" nebula." 

(b) This nebula, according to him, was a cloud of intensely 
heated gas (questionable). 

(c) Under the action of its own gravitation, the nebula 
assumed a form approximately globular, ivith a motion of rota- 
tion, the whirling motion depending upon the accidental differ- 
ences in the original velocities and densities of the different 



1 As to the origin of the nebula itself, he did not speculate. There was 
no assumption on his part, as is often supposed, that the matter was first 
created in the nebulous condition. He assumed only that as the egg may 
be taken as the starting-point in the life-history - of an animal," so the 
nebula is to be regarded as the starting-point of the life history of the 
planetary system. He did not raise the question whether the egg is older 
than the hen or not. 






296 laplace's nebular hypothesis. [§ 892 

parts of the nebula. As the contraction proceeded, the swift- 
ness of the rotation would necessarily increase for mechanical 
reasons. 

(d) In consequence of its whirling motion, the globe would 
necessarily become flattened at the poles, and ultimately, as 
the contraction went on, the centrifugal force at the equator 
would there become equal to gravity, and rings of nebulous 
matter would be detached from the central mass, like the rings 
of Saturn. In fact, Saturn's rings suggested this feature of 
the theory. 

(e) The ring thus formed would for a time revolve as a 
whole, but would ultimately break, and the material would col- 
lect into a globe revolving around the central nebula as a planet} 

Laplace supposed that the ring would revolve as if it were 
solid, the particles at the outer edge moving more swiftly than 
those at the inner (questionable). If this were always so, the 
planet formed would necessarily rotate in the same direction 
in which the ring had revolved. 

(/) The planet thus formed would throw off rings of its 
own, and so form for itself a system of satellites. 

393. This theory obviously explains most of the facts of the 
solar system, which were enumerated in the preceding article, 
though some of the exceptional facts (such as the short 
periods of the satellites of Mars, and the retrograde motions of 
those of Uranus and Neptune) cannot be explained by it alone 
in its original form. But even these exceptions do not contra- 
dict it, as is sometimes supposed. 

As to the modifications required by the theory, while they 
alter the mechanism of the development in some respects, they 
do not touch the main results. It is rather more likely, for 
instance, that the original nebula was a cloud of ice-cold dust 

1 It has been suggested by Hugging and others that the two small neb- 
ulae near the great nebula of Andromeda (Fig. 81) may be planets in 
process of formation. 



§ 393] LOCKYER's METEORITIC HYPOTHESIS. 297 

than incandescent gas and "fire-mist," to use a favorite expres- 
sion; and it is likely that planets and satellites were often 
separated from the mother-orb otherwise than in the form of 
rings. 

Nor is it possible that a thin, wide ring could revolve in 
the same way as a solid mass; the particles near the inner 
edge must make their revolution in periods much shorter than 
those upon the circumference, or the ring would tear to pieces. 
But this very fact makes it possible to account for the peculiar 
backward motion of the satellites of Uranus and Neptune, 
thus removing one of the main objections to the theory in its 
original form. 

Many things, also, make it questionable whether the outer 
planets are so much older than the inner ones, as Laplace's 
theory would indicate. It is not impossible that they may 
even be younger. 

Our limits do not permit us to enter into a discussion of Darwin's 
"tidal theory" of satellite formation, which maybe regarded as in a 
sense supplementary to the nebular hypothesis; nor can we more than 
mention Faye's proposed modification of it. According to him, the 
inner planets are the oldest. 

394. Lockyer's Meteoritic Hypothesis. — Within the last two 
years Mr. Lockyer has vigorously revived a theory which has 
been from time to time suggested before; viz., that all the 
heavenly bodies in their present state are mere clouds of 
meteors, or have been formed by the condensation of such 
clouds ; and it is an interesting fact, as Professor G. H. Dar- 
win has recently shown, that a large swarm of meteors, in 
which the individuals move swiftly in all directions, would, in 
the long run and as a whole, behave almost exactly, from a 
mechanical point of view, in the same way as one of Laplace's 
hypothetical gaseous nebulae. 1 

1 This is not very strange, after all. According to the modern "kinetic 
theory of gases " (Rolfe's "Physics," page 157), a meteor cloud is mochaui- 



-08 STARS, STAR-CLUSTERS, AND NEBULA. [§ 394 

The spectroscopic observations upon which Mr. Lockyer rests his 
attempted demonstration are many of them very doubtful; but that 
does not really discredit the main idea, except so far as the question 
of the origin and nature of the light of the heavenly bodies is con- 
cerned. He makes the light in all cases depend upon the collisions 
between the meteors, and finds in the spectra of the heavenly bodies 
evidence of the presence of materials with which we are familiar in the 
meteorites which fall upon the earth's surface. These identifications 
are in many cases questionable, — in some certainly incorrect, — and 
it seems much more likely that the luminosity depends to a great 
degree upon other than mere mechanical actions. 

395. Stars, Star-clusters, and Nebulae. — It is obvious that 
the nebular hypothesis in all its forms applies to the explana- 
tion of the relations of these different classes of bodies to 
each other. In fact, Hersehel, appealing only to the "law 
of continuity." had concluded, before Laplace published his 
theory, that the nebula? develop sometimes into clusters, some- 
times into double or multiple stars, and sometimes into single 
stars. He showed the existence in the sky of all the inter- 
mediate forms between the nebula and the finished star. For 
a time, about forty years ago, while it was generally .believed 
that all the nebulae were only star-clusters, too remote to be 
resolved by existing telescopes, his views fell rather into abey- 
ance ; but they regained acceptance in their essential features 
when the spectroscope demonstrated the substantial difference 
between gaseous nebulae and the star-clusters. 

396. Conclusions from the Theory ^f Heat. — Kant and La 
place, as Xeweomb says, seem to have reached their results by 
reasoning forwards. Modern science comes to very similar 

cally just the same thing as a mass of gas mag?}ijed. The kinetic theory 
asserts that gas is only a swarm of minute molecules, the peculiar gaseous 
properties depending upon the collisions of thes-e molecules with each 
other and with the walls of the enclosing vessel. MagAify sufficiently the 
molecules and the distances between them, and you have a meteoric cloud. 



§ 396] A GE OF THE SYSTEM. 299 

conclusions by working backwards from the present state of 
things. 

Many circumstances go to show that the earth was once 
much hotter than it now is. As we penetrate below the sur- 
face, the temperature rises nearly a degree (Fahrenheit) for 
every sixty feet, indicating a white heat at the depth of a few 
miles ; the earth at present, as Sir William Thomson says, " is 
in the condition of a stone that has been in the fire and has 
cooled at the surface." 

The moon bears apparently on its surface the marks of the 
most intense igneous action, but seems now to be entirely 
chilled. 

The planets, so far as we can make out with the telescope, 
exhibit nothing at variance with the view that they were once 
intensely heated, while many things go to establish it. Jupi- 
ter and Saturn, Uranus and Neptune, do not seem yet to have- 
cooled off to anything like the earth's condition. 

As to the sun, we have in it a body continuously pouring 
forth an absolutely inconceivable quantity of heat without any 
visible source of supply. As has been explained already (Art. 
192), the only rational explanation of the facts, thus far pre- 
sented, is that which makes it a huge, cloud-mantled ball of 
elastic substance, slowly shrinking under its own central grav- 
ity, and thus generating heat. 1 A shrinkage of about 300 feet 
a year in the sun's diameter will account for the whole annual 
output of radiant heat and light. 

397. Age of the System. — Looking backward, then, and 
trying to imagine the course of time and of events reversed, 
we see the sun growing larger and larger, until at last it has 

1 So far we have no decisive evidence whether the sun has passed its 
maximum of temperature or not. Mr. Lockyer thinks its spectrum 
(resembling as it does that of Capella and the stars of the second class) 
proves that it is now on the doicnward grade and growing cooler ; but 
others do not consider the evidence conclusive. 



300 FUTURE DURATION OF THE SYSTEM. [§ 39 ? 

expanded to a huge globe that fills the largest orbit of our 
system. How long ago this may have been, we cannot state 
with certainty. If we could assume that the amount of heat 
yearly radiated by the solar surface had remained constantly 
the same through all those ages, and, moreover, that all the 
radiated heat came solely from the slow contraction of the 
sun's mass, apart from any considerable original capital in 
the form of a high initial temperature, and without any re- 
enforcement of energy from outside sources, — if we could 
assume these premises, it is easy to show that the sun's past 
history must cover about 15,000000 or 20,000000 years. But 
such assumptions are at least doubtful ; and if we discard 
them, all that can be said is that the sun's age must be 
greater, and probably many times greater, than the limit we 
have named. 

398. Future Duration of the System. — Looking forward, 
on the other hand, from the present towards the future, it i3 
easy to conclude with certainty that if the sun continues its 
present rate of radiation and contraction, and receives no sub- 
sidies of energy from without, it must, within 5,000000 or 
10,000000 years, become so dense that its constitution will be 
radically changed. Its temperature will fall and its function 
as a sun will end. Life on the earth, as we know life, will be 
no longer possible when the sun has become a dark, rigid, 
frozen globe. At least this is the inevitable consequence of 
what now seems to be the true account of the sun's condition 
and activity. 

399. The System not Eternal. — One conclusion seems to 
be clear : That the present system of stars and worlds is 
not an eternal one. We have before us everywhere evidence 
of continuous, irreversible progress from a definite beginning 
towards a definite end. Scattered particles and masses are 
gathering together and condensing, so that the great grow con- 



§399] THE SYSTEM NOT ETERNAL. 301 

tinually larger by capturing and absorbing the smaller. At 
the same time the hot bodies are losing their heat and distrib- 
uting it to the colder ones, so that there is an unremitting 
tendency towards a uniform, and therefore useless, temperature 
throughout our whole universe : for heat is available as energy 
(i.e., it can do ivork) only when it can pass from a warmer 
body to a colder one. The continual warming up of cooler 
bodies at the expense of hotter ones always means a loss, 
therefore, not of energy, — for that is indestructible, — but of 
available energy. To use the ordinary technical term, energy 
is continually "dissipated" by the processes which constitute 
and maintain life on the universe. This dissipation of energy 
can have but one ultimate result, that of absolute stagnation 
when the temperature has become everywhere the same. 

If we carry our imagination backwards, we reach " a begin- 
ning of things," which has no intelligible antecedent ; if for- 
wards, we come to an end of things in dead stagnation. That 
in some way this end of things will result in a " new heavens 
and a new earth" is, of course, probable, but science as yet 
can present no explanation of the method. 

Note to Article 361. New Variables and Variable-star Clusters. 

Since the summer of 1895 there has been a rapid increase in the 
number of known variables, largely as the result of the examination 
of photographs of different portions of the sky made at Cambridge, 
U. S., and at Arequipa. About thirty variables have thus been 
brought to light, among them one star of the Algol type. 

Mr. Chandler, from visual observations, has detected a variable of 
the Beta Lyrse type, designated as U, Pegasi, which is interesting 
as having a period of only 5 h 31 m , by far the shortest known. 

All these new variables are too small to be visible to the naked 
eye, and all except the Algol variables show peculiar banded spectra, 
generally with bright lines in them. 

In 1893 and 1895 three small " temporary " stars were found upon 
the Arequipa plates, indicating that the appearance of such stars is 



302 VARIABLE-STAR CLUSTERS. 

not very unusual, though only a few become bright enough to be 
seen without a telescope. 

But the most remarkable discovery is that of variable-star clus- 
ters. Several have been found, but the most remarkable thus far 
are the two known as Messier 3 and Messier 5. In the first no less 
than 96 variables have been detected, and in the second nearly 60. 
In Messier 5 the changes are so rapid that the comparison of photo- 
graphs taken only two hours apart brings them out very strikingly. 



APPENDIX. 

CHAPTER XIII 

ASTRONOMICAL INSTRUMENTS. 

THE CELESTIAL GLOBE. — THE TELESCOPE: SIMPLE, ACHRO- 
MATIC, AND REFLECTING. — THE EQUATORIAL. — THE 

FILAR MICROMETER,. THE TRANSIT INSTRUMENT. 

THE CLOCK AND CHRONOGRAPH. — THE MERIDIAN CIR- 
CLE. — THE SEXTANT. 

400. The Celestial Globe. — The celestial globe is a ball, 
usually of papier-m&che, upon which are drawn the circles of 
the celestial sphere and a map of the stars. It is ordinarily 
mounted in a framework which represents the horizon and the 
meridian, in the manner shown in Fig. 83. 

The "horizon/' HH ! in the figure, is usually a wooden 
ring three or four inches wide and perhaps three-quarters of 
an inch thick, directly supported by the pedestal. It carries 
upon its upper surface at the inner edge a circle marked with 
degrees for measuring the azimuth of any heavenly body, and 
outside this the so-called zodiacal circles, which give the sun's 
longitude and the equation of time for every day of the year. 

The meridian ring, MM 1 , is a circular ring of metal whiqh 
carries the bearings upon which the globe revolves. Things 
are so arranged, or ought to be, that the mathematical axis 
of the globe is exactly in the same plane as the graduated face 



304 



APPENDIX. 



[§400 



of the ring, which is divided into degrees. The meridian ring 
is held underneath the globe by a support, with a clamp which 
enables us to fix it securely in any desired position. 

The surface of the globe is marked first with the celestial 
equator, next with the ecliptic, crossing the equator at an 




Fig. 83. — The Celestial Globe. 



angle of 23 }° at F(as the figure is drawn, V happens to be the 
autumnal equinox, not the vernal), and each of these circles is 
divided into degrees. The equinoctial and solstitial colures 
are also always represented. As to the other circles, usage 
differs. The ordinary way at present is to mark the globe 
with twenty-four hour-circles 15° apart (the colures, Art. 117, 
being four of them), and with parallels of declination 10° 



§400] TO RECTIFY A GLOBE. 305 

apart. On the surface of the globe are plotted the positions 
of the stars and the outlines of the constellations. 

It is perhaps worth noting that x. any of the spirited figures of the 
constellations upon our present globes are copied from designs drawn 
by Albert Diirer for a star-map published in his time. 

The Hour-index is a small circle of thin metal, about four 
inches in diameter, which is fitted to the northern pole of the 
globe with a stiflish friction, so that it can be set like the 
hands of a clock, and when once set will turn with the globe 
without shifting. 

401. To rectify a Globe, — i.e., to set it so as to show the 
aspect of the heavens at any time : — 

(1) Elevate the north pole of the globe to an angle equal 
to the observer's latitude by means of the graduation on 
the meridian ring, and clamp the ring securely. 

(2) Look up the day of the month on the horizon of the 
globe, and opposite to the day find on the zodiacal circle the 
sun's longitude for that day. 

(3) On the ecliptic (upon the surface of the globe) find 
the degree of longitude thus indicated, and bring it to the 
graduated face of the meridian ring. The globe is thus set to 
correspond to apparent noon of the day in question. 

It may be well to mark the place of the sun temporarily with a bit 
of paper gummed on at the proper place in the ecliptic. It can easily 
be wiped off after using. 

(4) Hold the globe fast, so as to keep the place of the sun 
exactly on the meridian, and turn the hour -index until it shows 
at the edge of the meridian ring the mean time of apparent 
noon (i.e., 12 h ± the equation of time given on the wooden 
horizon for the day in question). 

If standard time is used, the hour-index must be set to the standard 
time for apparent noon instead of the local mean time. 



300 APPENDIX. [§401 

(5) Finally* turn the globe upon its axis until the hour* 
index shows at the meridian the hour for which it is to be 
set. The globe will then represent the true aspect of the 

heavens at that time. 

The positions of the moon and planets are not given by this opera- 
tion, since they have no fixed places in the sky, and therefore cannot 
be put in by the globe-maker. If one wants them represented, he 
must look up their right ascensions and declinations in some almanac, 
and mark the proper places on the globe with bits of wax or paper. 



TELESCOPES. 

402. Telescopes are of two kinds, — refracting and reflecting. 
The refractor was first invented, early in the seventeenth 

century, and is much more used, but the largest instruments 
ever made are reflectors. In both, the fundamental principle 
is the same. The large lens of the instrument (or else its 
concave mirror) forms a real image of the object looked at, 
and this image is then examined and magnified by the eye- 
piece, which in principle is only a magnifying-glass. 

In the form of instrument, however, which was originally devised 
by Galileo and is still used as the "opera-glass," the rays from the 
object-glass are intercepted, and brought to parallelism, by the concave 
lens which serves as an eye-glass, before they form the image. Tele- 
scopes of this construction are never made of much power, being 
inconvenient on account of the smallness of the field of view. 

403. The Simple Refracting Telescope. — This consists 
essentially, as shown in Fig. 84, of two convex lenses : one, 
the object-glass A, of large size and long focus ; the other, the 
eye-glass B, of short focus, — the two being set at a distance 
nearly equal to the sum of their focal lengths. Recalling the 
optical principles relating to the formation of images by lenses, 
we see that if the instrument is pointed towards the moon, for 
instance, all the rays that strike the object-glass from the fop 



§403] MAGNIFYING POWER. 307 

of the crescent will be collected to a focus at a, while those 
from the bottom will come to a focus at b ; and similarly with 
rays from the other points on the surface of the moon. We 
shall, therefore, get in the " focal plane " of the object-glass a 
small inverted "image" of the moon. The image is a real 



CL 



s — y u -— yfj ' 

Fig. 84. — The Simple Refracting Telescope. 



one; i.e., the rays really meet at the focal points, so that if we 
insert a photographic plate in the focal plane at ab and prop- 
erly expose it, we shall get a picture of the object. The size 
of the picture will depend upon the apparent angular diameter 
of the object and the distance from the object-glass to the 
image ab. 

Tf the focal length of the lens A is ten feet, then the image of the 
moon will be a little more than one inch in diameter. 

404. Magnifying Power. — If we use the naked eye, we 
cannot see the image distinctly from a distance much less than 
a foot, but: if we use a magnifying lens of, say, one inch focus, 
we can .view it from a distance of only an inch, and it will 
look correspondingly larger. Without stopping to prove the 
principle, we may say that the magnifying power is simply 
equal to the quotient obtained by dividing the focal length of the 
object-glass :by that of the. eye-lens. [ 

It is to be note d, however, that a magnifying power of '^unityjs 
sometimes, spoken of as no magnifying power at all, since the. image 
appears of the same size as the object. ..... 

The magnifying power of a telescope is changed at pleasure by 
simply interchanging the eye-pieces, of which revery telescope of any 
pretensions always has a considerable stock, giving various powers. 



308 APPENDIX. [§ 405 

405. Brightness of the Image. — This depends not upon the 
focal length of the object-glass, but upon its diameter; or, 
more strictly, its area. If we estimate the diameter of the 
pupil of the eye at one-fifth of an inch, as it is usually reck- 
oned, then (neglecting the loss from want of perfect transpar- 
ency in the lenses) a telescope one inch in diameter collects 
into the image of a star 25 times as much light as the naked 
eye receives; and the great Lick telescope of 36 inches in 
diameter, 32,400 times as much, or about 30,000 after allow- 
ing for the losses. The amount of light is proportional to the 
square of the diameter of the object-glass. 

The apparent brightness of an object which, like the moon or 
a planet, shows a disc, is not, however, increased in any such 
ratio, because the light gathered by the object-glass is spread 
out by the magnifying power of the eye-piece. But the total 
quantity of light in the image of the object greatly exceeds 
that which is available for vision with the naked eye, and 
objects which, like the stars, are mere luminous points, have 
their brightness immensely increased, so that with the tele- 
scope millions otherwise invisible are brought to light. "With 
the telescope, also, the brighter stars are easily seen in the 
daytime. 

406. The Achromatic Telescope. — A single lens cannot 
bring the rays which emanate from a single point in the object 
to any exact focus, since the rays of each different color are 
differently refracted, — the blue more than the green, and this 
more than the red. In consequence of this so-called " chro- 
matic aberration," the simple refracting telescope is a very 
poor 1 instrument. 

1 By making it extremely long in proportion to its diameter, the indis- 
tinctness of the image is considerably diminished, and in the middle of the 
seventeenth century instruments more than 100 feet in length were used 
by Huyghens and others. Saturn's rings and several of his satellites were # 
discovered with instruments of this kind. 



§ 406] ACHROMATISM NOT PERFECT. 309 

About 1760, it was discovered in England that by making 
the object-glass of two or more lenses of different kinds of 
glass, the chromatic aberration can be nearly corrected. Object- 
glasses so made — none others are now in common use — are 
called achromatic. In practice, only two lenses are ordinarily 
used in the construction of an astronomical glass, — a convex 
of crown glass, and a concave of flint glass, the curves of the 
two lenses and the distances between them being so chosen as 
to give the most perfect possible correction of the " spherical " 
aberration (" Physics," p. 363) as well as of the chromatic. 

407. Achromatism not Perfect. — It is not possible with the 
kinds of glass hitherto available to obtain a perfect correction 
of color. Even the best achromatic telescopes show a purple 
halo around the image of a bright star, which, though usually 
regarded as "very beautiful" by tyros, seriously injures the 
definition, and is especially obnoxious in large instruments. 

This imperfection of achromatism makes it impossible to get satis- 
factory photographs with an ordinary object-glass, corrected for vision. 
An instrument for photography must have an object-glass specially 
corrected for the purpose, since the rays most efficient in impressing 
the image upon the photographic plate are the blue and violet rays, 
which in the ordinary object-glass are left to wander very wildly. 

Much is hoped from the new kinds of glass now being made for 
optical purposes at Jena, Germany, as the results of the experiments 
conducted by Professor Abbe at the expense of the German govern- 
ment. Though the new glass is especially intended for use in the con- 
struction of microscopes, a few telescope lenses from three to six inches 
in diameter have been already made with it, which appear to be nearly 
perfect in their color correction. 

408. Diffraction and Spurious Discs. — Even if a lens were 
absolutely perfect as regards the correction of aberrations, 
both spherical and chromatic, it would still be unable to give 
vision absolutely distinct. Since light consists of waves of 
finite length, the image of a luminous point can never be also 



310 



APPENDIX. 



[§408 



a point, but must of mathematical necessity be a disc of finite 
diameter surrounded by a series of ' diffraction ? rings. The 
diameter of the " spurious disc" of a star, as it is called, 
varies inversely with the diameter of the object-glass : the 
larger the telescope, the smaller the image of a star with a 
given magnifying power. 

With a good telescope and a power of about 30 to the inch of aper- 
ture (120 for a 4-inch telescope) the image of a star, when the air is 
steady (a condition unfortunately seldom fulfilled), should be a clean, 
round disc, with a bright ring around it, separated from the disc by 
a clear black space. According to Dawes, the disc of a star with a 
4J-inch telescope should be about 1" in diameter; with a 9-inch instru- 
ment 0".5, and \ n for a 36-inch glass. 



Eamsden 
(Positive) 



Huyghenian 
(Negative) 

( || **&^ — IT' 



Fig. 85. 



Telescope Eye-pieces, 



409. Eye-pieces. — For some purposes the simple convex 
lens is the best " eye-piece " possible ; but it performs well 
only for a small object, like a close double star, placed exactly 

in the centre of the field of 
view. Generally, therefore, we 
employ " eye-pieces " composed 
of two or more lenses, which 
give a larger field of view than 
a single lens, and define satis- 
factorily over the whole extent 
of the field. They fall into two general classes, the positive 
and the negative. 

The positive eye-pieces are much more generally useful. They act 
as simple magnifying-glasses, and can be taken out of the telescope 
and used as hand-magnifiers if desired. The image of the object 
formed by the object-glass lies outside o/this kind of eye-piece, between 
it and the object-glass. 

In the negative eye-piece, on the other hand, the rays from the 
object-glass are intercepted by the so-called " field-lens " before reach- 
ing the focus, and the image is formed between the two lenses of the 
eye-piece. It cannot therefore be used as a hand-magnifier. 

Fig. 85 shows the two most usual forms of eye-piece. 



§ 409] THE REFLECTING TELESCOPE. 311 

These eye-pieces show the object in an inverted position; 
but this is of no importance as regards astronomical obser- 
vations. 

410. Reticle. — When the telescope is used for pointing 
upon an object, as it is in most astronomical instruments, it 
must be provided with a ' reticle ' of some sort. The simplest 
form is a metallic frame with spider lines stretched across it, 
the intersection of the spider lines being the point of reference. 
This reticle is placed not at or near the object-glass, as is often 
supposed, but -in its focal plane, as ab in Fig. 84. Sometimes a 
glass plate with fine lines ruled upon it is used instead of 
spider lines. Some provision must be made for illuminating 
the lines, or " wires," as they are usually called, by reflecting 
into the instrument a faint light from a lamp suitably placed. 

411. The Reflecting Telescope. — About 1670, when the 
chromatic aberration of refractors first came to be understood 
(in consequence of Xewton's discovery of the " decomposition 
of light "), the reflecting telescope was invented. For nearly 
150 years it held its place as the chief instrument for star- 
gazing, until about 1820, when large achromatics began to be 
made. There are several varieties of reflecting telescope, dif- 
fering in the way in which the image formed by the mirror is 
brought within reach of the magnifying eye-piece. 

Until about 1870, the large mirror (technically " speculum ") 
was always made of speculum metal, a composition of copper 
and tin. It is now usually made of glass, silvered on the front 
by a chemical process. When new, these silvered films reflect 
much more light than the old speculum metal : they tarnish 
rather easily, but fortunately can be easily renewed. 

412. Large Telescopes. — The largest telescopes ever made have 
been reflectors. At the head stands the enormous instrument of Lord 
Rosse of Birr Castle, Ireland, six feet in diameter and sixty feet long, 



312 APPENDIX. [§ 412 

made in 1842, and still used. Next in size, but probably superior in 
power, comes the five-foot silver-on-glass reflector of Mr. Common, at 
Ealing, England, completed in 1889 ; and then follow a number (four 
or five) of four-foot telescopes, — that of Herschel (erected in 1789, but 
long ago dismantled) being the first, while the great instrument at 
Melbourne is the only instrument of this size now in active use. 

Of the refractors, the largest is that of the Yerkes Observatory at 
Lake Geneva, Wisconsin, with an object-glass 40 inches in diameter, 
and a tube nearly 70 feet long. The next in size is the telescope of 
the Lick Observatory (see frontispiece), which has an aperture of 36 
inches. Next to this come the great telescopes at Pulkowa, Meudon 
and Mce, with apertures of about 30 inches ; the Vienna telescope, 
27 inches ; the tw 7 o telescopes at Washington and the University of 
Virginia, 26 J inches ; and four or five others with apertures of from 
26 to 23 inches, at Cambridge (England), Greenwich, Paris and 
Princeton. Most of these large object-glasses were made by the 
Clarks of Cambridge (U.S.). 

413. Relative Advantages of Reflectors and Refractors. — 

There is no little discussion on this point, each form of instrument 
having its earnest partisans. 

In favor of the reflector we have first, its cheapness and com- 
parative ease of construction, since there is but one surface to grind and 
polish, as against four in an achromatic object-glass ; second, the fact 
that reflectors can be made larger than refractors; third, the reflector 
is absolutely achromatic. 

On the other hand, a refractor gives a much brighter image than a 
reflector of the same size; it also generally defines much better, 
because, for optical reasons into which w T e cannot enter here, any 
slight distortion or malformation of the speculum of a reflector dam- 
ages the image many times more than the same amount of distortion 
of an object-glass. Then a lens hardly deteriorates at all with age, 
while a speculum soon tarnishes, and must be re-silvered or re-polished 
every few years. 

As a rule, also, refractors are lighter and more convenient than 
reflectors of equal power. 



§414] 



MOUNTING OF A TELESCOPE. 



313 



414. Mounting of a Telescope, — the Equatorial. — A tele- 
scope, however excellent optically, is not good for much unless 
firmly and conveniently mounted. 1 

At present some form of equatorial mounting is practically 
universal. Fig. 86 represents schematically the ordinary ar- 
rangement of the instrument. Its essential feature is that its 
"principal axis " (i.e., the one which turns in fixed bearings 
attached to the pier, and is called the polar axis) is placed par- 
allel to the earth's axis, pointing to 
the celestial pole,^so that the circle 
H, attached to it, is parallel to the 
celestial equator. This circle is 
sometimes called the hour-circle, 
sometimes the right-ascension circle. 
At the extremity of the polar axis a 
" sleeve " is fastened, which carries 
within it the declination axis D, 
and to this declination axis is at- 
tached the telescope tube T, and 
also the declination circle C. 

The advantages of this mount- 
ing are very great. In the first 
place, when the telescope is once 
pointed upon an object, it is not 
necessary to move the declination axis at all in order to keep 
the object in the field, but only to turn the polar axis with a 
perfectly uniform motion, which motion can be, and usually is, 
given by clock-work (not shown in the figure). 

In the next place, it is very easy to find an object even if 




Fig. 86. — The Equatorial. 



1 We may add that it must, of course, be mounted where it can be 
pointed directly at the stars, without any intervening window- glass be- 
tween it and the object. We have known purchasers of telescopes to 
complain bitterly because they could not see Saturn well through a closed 
window. 



314 



APPENDIX. 



[§414 



invisible to the eye (like a faint comet, or a star in the day- 
time), provided we know its right ascension and declination, 
and have the sidereal time, — a sidereal clock or chronometer 
being an indispensable accessory of the instrument. 

The frontispiece shows the actual mounting of the Lick telescope. 
Fig. 71, Art. 337, represents another form of equatorial mounting, 
which has been adopted for the instruments of the photographic 
campaign. 

415. The Micrometer. — This is an instrument for measur- 
ing small angles, usually not exceeding 15' or 20'. Various 

kinds are employed, all of 
them small pieces of ap- 
paratus, which, when used, 
are secured to the eye-end 
of a telescope. The most 
common is the parallel- 
wire micrometer, which is 
a pair of parallel spider 
threads, one or both of 
which can be moved with 
a fine screw with a grad- 
uated head, so that the 
distance between the two 
' wires ? can be varied at 
pleasure, and then " read 
off" by looking at the 
micrometer head. Fig. 87 
represents such an instru- 
ment attached to a telescope : the spider threads are in the 
box BB, and are viewed through the eye-piece. 

416. The Transit Instrument (Fig. 88). — This consists of 
a telescope carrying at the eye-end a reticle, and mounted on 
a stiff axis with pivots that are perfectly true. They turn in 




Fig. 87. — The Filar Position Micrometer. 



§416] 



THE ASTRONOMICAL CLOCK, ETC. 



815 



Y's, which are firmly set upon some sort of framework or on 
the top of solid piers, and so placed that the axis will be ex- 
actly east and west and precisely level. When the telescope 
is turned on its axis, the mid- 
dle wire of the reticle, if 
everything is correctly ad- 
justed, will follow the celes- 
tial meridian, and whenever a 
star crosses the wire, we know 
that it is exactly on the me- 
ridian. Instead of a single 
wire, the reticle generally con- 
tains a number of wires 
equally spaced, as shown in 
Fig. 89. The object is then 
observed upon each of the 
wires, and the mean of the 
observations is taken as giv- 
ing the moment when the star crossed the middle wire. 

A delicate spirit-level, to be placed 
on the pivots and test the horizon- 
tally of the axis, is an indispensable 
accessory. 

So far as the theory of the instru- 
ment is concerned, a graduated circle 
is not essential ; but practically it is 
necessary to have one attached to 
the axis in order to enable the ob- 
server to set for a star in preparing 

Fig. 89. — Reticle of the Transit r r o 

instrument. for the observation. 




Fig. i 



- The Transit Instrument. 




417. The Astronomical Clock, Chronometer, and Chrono- 
graph. — A good timepiece is an essential adjunct of the tran- 
sit instrument, and equally so of most other astronomical 
instruments. The invention of the pendulum clock by Huy- 



316 APPENDIX. [§ 417 

ghens was almost as important an event in the history of 
practical astronomy as that of the telescope itself. 

The astronomical clock differs in no essential respect from 
any other, except that it is made with extreme care, and has a 
" compensated " pendulum so constructed that the rate of the 
clock will not be affected by changes of temperature. It is 
almost invariably made to beat seconds, and usually has its 
face divided into twenty-four hours instead of twelve. 

Excellence in a clock consists essentially in the constancy of 
its 'rate^ ; i.e., it should gain or lose precisely the same amount 
each day, and as a matter of convenience the daily rate should 
be small, not to exceed a second or two. The rate is adjusted 
by slightly raising or lowering the pendulum bob, or putting 
little weights upon a small shelf attached to the rod ; — the 
' error/ when necessary, by simply setting the hands. 

The error of a timepiece is the difference between the time shown 
by the clock-face and the true time at the moment ; the rate is the 
amount it gains or loses in twenty-four hours. 

The chronometer is simply a carefully made watch, and has 
the advantage of portability, though in accuracy it cannot 
quite compete with a well-made clock. 

Formerly transit-instrument observations were made by sim- 
ply noting with eye and ear the time indicated by the clock at 
the moment when the star observed was crossing the wire or 
reticle. A skilful observer can do this within about a tenth 
of a second. At present the observer usually presses a tele- 
graph-key at the moment of the transit, and so telegraphs 
the instant to an instrument called a "chronograph" which 
makes a permanent record of the observation upon a sheet 
of paper, — thus making the observation much more accurate 
as well as easier. (For the description of the chronograph, 
see General Astronomy, Art. 56.) 

418. The Meridian Circle. — In many respects this is the 
fundamental instrument of a working observatory. It is 



§418] 



THE MERIDIAN CIRCLE. 



317 



simply the transit instrument plus a finely graduated circle 
or circles attached to the axis, and provided with microscopes 
for reading the graduation with precision. In the accurate 
construction of the pivots 
of the instrument and of 
the circles, with their 
graduation, the utmost re- 
sources of the mechanical 
art are taxed. Fig. 90 
shows the instrument in 
principle. Fig. 91 is a 
small meridian circle, as 
actually constructed, with jjf* 
a four-inch telescope and 
twenty-four-inch circles. 

Its main purpose is to 
determine the right ascen- 
sion and declination of ■ 
objects as they cross the 
meridian. The declination is determined by measuring how 
many degrees the object is north or south of the celestial equa- 
tor at the moment of transit. The " circle-reading " for the 
equator must first be determined as a zero point; and this is 
done by observing a star near the pole and getting the circle- 
reading as it crosses the meridian above the pole, and twelve 
hours later, when it crosses again below it. The mean of these 
two readings, corrected for refraction, will be the circle-reading 
for the pole, or the polar point, which is, of course, just 90* 
from the equatorial zero point. 




Fig. 90. — The Meridian Circle (Schematic). 



419. The Nadir Point. — To get the latitude of the observer 
with this instrument (Art. 81), it is necessary also to have the 
nadir point as a zero ; i.e., the circle-reading which corresponds 
to the vertical position of the telescope. This point is found 
by pointing the telescope down towards a basin of mercury 



318 



APPENDIX. 



[§419 



beneath it, and setting it so that the image of the east and 
west wire in the reticle coincides with itself. Then the tele- 
scope will be exactly vertical. The horizontal point is just 
90° from the nadir point, and the difference between the 




Fin. oi.— A Meridian Circle. 



(north) horizontal point and the polar point is the latitude of 
the observatory. 

Obviously the instrument can also be used as a simple tran- 
sit instrument in connection with a clock, so that (Art, 99) the 



§419] 



THE SEXTANT. 



319 



observer can determine both the right ascension and declination 
of any object which is visible when it crosses the meridian. 

420. The Sextant. — All the instruments so far mentioned, 
except the chronometer, require firmly fixed supports, and are, 
therefore, useless at sea. The sextant is the only instrument 
for measurement upon which the mariner can rely. By means 
of it he can measure the angular tjjstance between any two 
points (as, for instance, the sun and the visible horizon), not 




Fig. 92. — The Sextant. 

by pointing first on one and afterwards on the other, but by 
sighting them both simultaneously and in apparent coincidence. 
This observation can be accurately made even if he has no 
stable footing, but is swinging about on the deck of a vessel. 
Fig. 92 represents the instrument. For a detailed description 
and explanation, see General Astronomy, Arts. 76-80. 

421. Use of the Instrument. — The principal use of the in- 
strument is in measuring the altitude of the sun. At sea, an 



320 APPENDIX. [§ 421 

observer holding the instrument in his right hand, and keep- 
ing the plane of the arc vertical, looks directly towards the 
visible horizon through the horizon-glass, H, at the point under 
the sun. Then by moving the index, N, with his left hand, 
he inclines the index mirror upward, until he sees the re- 
flected image of the sun, and the lower edge of this image is 
brought to touch the horizon-line. The reading of the gradu- 
ation, after due correction for refraction, etc., gives the sun's 
true altitude at the moment. If the observation is made near 
noon, for the purpose of determining the latitude, it will not 
be necessary to read the chronometer at the same time. If, 
however, the observation is made for the purpose of determin- 
ing the longitude (Art. 497), the instant of observation, as 
shown by the chronometer, must be carefully noted. 

The skilful use of the sextant requires considerable dexterity, 
and from the small size of the telescope, the angles measured 
are less precisely measured than with large fixed instruments ; 
but the portability of the instrument and its applicability at 
sea render it absolutely invaluable. It was invented by 
Gregory, of Philadelphia, in 1730, but an earlier design of an 
instrument on the same principle has been found (unpublished) 
among the papers of Newton. 



§422] HOUR-ANGLE AND TIME. 321 



CHAPTER XIV. 

MISCELLANEOUS. 

HOUR-ANGLE AND TIME. — TWILIGHT. — DETERMINATION 
OF LATITUDE. — SHIP'S PLACE AT SEA. — FINDING THE 
FORM OF THE EARTH'S ORBIT. — THE ELLIPSE. — ILLUS- 
TRATIONS of kepler's third law. — the equation 

OF LIGHT AND THE SUN'S DISTANCE. — ABERRATION OF 
LIGHT. — DE L'lSLE's METHOD OF GETTING THE SOLAR 
PARALLAX FROM THE TRANSIT OF YENUS. — THE 
CONIC SECTIONS. — STELLAR PARALLAX. — 

422. Hour-angle and Time (supplementary to Arts. 89-91). 
— There is another way of looking at the matter of time, 
which has great advantages. If we face towards the north 
pole and consider the star m (Fig. 93) as carried at the end 
of the arc mP of the hour-circle, which connects it to the 
pole, we may regard this arc as a sort of clock-hand ; and if 
we produce it to the celestial equator and mark off the equa- 
tor into 15° spaces, or ' hours/ the angle QPm, or the arc Q F, 
will measure the time which has elapsed since m was on the 
meridian PQ. The angle mPQ is called the hour -angle of the 
star m. It is the angle at the pole between the meridian and 
the hour-circle which passes through the body. 

Having now this definition of the hour-angle, we may define 
sidereal time (Art. 91) at any moment as the hour-angle of the 
vernal equinox at that moment. In the same way, the apparent 
solar time (Art. 88) is the hour-angle of the sun's centre ; the 



322 



APPENDIX. 



[§422 




Fig. 93. — Hour-Angle. 



mean solar time (Art. 89) is the hour-angle of a fictitious sun 
which moves around the heavens uniformly, once a year, in 

the equator, keeping its 
right ascension equal to the 
mean longitude of the real 
sun. For some purposes, 
as in dealing with the tides, 
it is convenient to use lunar 
time, which is simply the 
hour-angle of the moon at 
any moment. 

423. Twilight is caused 
by the reflection of sunlight 
from the upper portions of the 
earth's atmosphere. After the 
sun has set, its rays still con- 
tinue to shine through the air above the observer's head, and twilight 
continues as long as any portion of this illuminated air can be seen 
from where he stands. It is considered to end when stars of the 
sixth magnitude become visible near the zenith, which does not occur 
until the sun is about 18° below the horizon ; but this is not strictly 
the same for all places. 

The duration of twilight varies with the season and with the 
observer's latitude. In latitude 40° it is about 90 minutes on March 
1st and Oct. 12th ; but more than two hours at the summer solstice. 
In latitudes above 50°, when the days are longest, twilight never quite 
disappears, even at midnight. On the mountains of Peru, on the 
other hand, it is said never to last more than half an hour. 

424. Methods of determining Latitude by Other Observa- 
tions than those of Circumpolar Stars (supplementary to Art. 
81). — To determine the latitude by observations of a circum- 
polar star, the observer must remain at the same station at 
least twelve hours. The latitude can be determined, however, 
with a good instrument, with almost equal precision, by ob- 
serving the meridian altitude, or zenith distance, of a body whose 



§ 424] DETERMINATION OF LATITUDE. 323 

declination is accurately knoivn. In Fig. 94 the circle AQPB 

is the meridian, Q and P being respectively the equator and 

the pole, and Z the zenith. QZ is evidently the declination 

of the zenith (i.e., the distance of 

the zenith from the celestial ^^ 

equator) and is equal to PB, the OS 

latitude of the observer, or height s/ \ 

of the pole. Suppose now that / \^ 

we observe Zs, i.e., the zenith ^[ x 

distance of the star s, south of 

the zenith, as it Crosses the me- ^ig. 94. -Determination of Latitude. 

ridian, and that we know Qs, the declination of the star. 
Evidently QZ = Qs + sZ\ i.e., the latitude equals the declina- 
tion of the star plus its zenith distance. If the star were at s', 
south of the equator, the same equation would hold good 
algebraically, because the declination, Qs', is a minus quantity. 
If the star were at n, between the zenith and the pole, we 
should have : Latitude equals the declination of the star minus 
the zenith distance. This is the method actually used at sea 
(Art. 426), the sun being the object observed. 

There are many other methods in use, as, for instance, that 
by the zenith telescope and that by the prime-vertical instru- 
ment, which are practically more convenient and more accurate 
than either of the two described, but they are more compli- 
cated, and their explanation would take us too far. The 
reader is referred to General Astronomy, Arts. 104-107. 

FINDING THE PLACE OF A SHIP. 

425. The determination of the place of a ship at sea is, 
from the economic point of view, the most important problem 
of Astronomy. National observatories and nautical almanacs 
were established, and are maintained, principally to supply the 
mariner with the data needed to make this determination 
accurately and promptly. The methods employed are neces- 



324 APPENDIX. [§ 42 5 

sarily such that the required observations can be made with 
the sextant and chronometer, since fixed instruments, like the 
transit instrument and meridian circle, are obviously out of 
the question on board a vessel. 

426. Latitude at Sea. — This is obtained by observing with 
the sextant the sun's maximum altitude, which is reached 
when the sun is crossing the meridian. 

Since at sea the sailor seldom knows beforehand the precise 
time which will be shown by his chronometer at noon, he 
takes care not to be too late, and begins to measure the sun's 
altitude a little before noon, repeating his observations every 
minute or two. At first the altitude will keep increasing, but 
when noon comes the sun will cease rising, and then begin to 
descend. The observer uses, therefore, the maximum altitude 
obtained, which, with due allowance for refraction and some 
other corrections (for details, see larger works) gives him the 
true altitude of the sun's centre. Taking this from 90°, we 
get its zenith distance. 

Referring now to Fig. 94, in which the circle AQZPB is 
the meridian, P the pole, Z the zenith, and OQ the celestial 
equator seen edgewise, we see that PB, the altitude of the 
pole, is necessarily equal to ZQ, the distance from the zenith 
to the equator. Now from the almanac we find the declina- 
tion of the sun, Qs, for the day on which the observations are 
made. 1 We have only to add to this, Zs, the measured dis- 
tance of the sun from the zenith, to obtain QZ, which is the 
observer's latitude. 

It is easy in this way, with a good sextant, to get the lati- 
tude within about half a minute of arc, or, roughly, about 
half a mile, which is quite sufficiently accurate for nautical 
purposes. 

1 If the sun happened to be south of the equator (in the winter), as at 
s', we should haveZ"<j) equals Zs — s f Q. 



§ 427] LOCAL TIME AND LONGITUDE AT SEA. 325 

427. Determination of Local Time and Longitude at Sea. 

— The usual method now employed for the longitude depends 
upon the chronometer. This is carefully ' rated ' in port; 
i.e., its error and its daily gain or loss are determined by com- 
parisons with an accurate clock for a week or two, the clock 
itself being kept correct to Greenwich time by transit obser- 
vations. By merely allowing for the gain or loss since leaving 
port, and adding this gain or loss to the ' error ' (Art. 417), 
which the chronometer had when brought on board, the sea- 
man at once obtains the error of the chronometer on Green- 
wich time at any moment ; and allowing for this error, he has 
the GreenivicJi time itself, with an accuracy which depends 
only on the constancy of the chronometer's rate : it makes no 
difference whether it is gaining much or little, provided its 
daily rate is steady. 

He must also determine his own local time ; and this must 
be done with the sextant, since, as was said before, an instru- 
ment like the transit cannot be used at sea. He does it by 
measuring the altitude of the sun, not at or near noon, as often 
supposed, but when the sun is as near due east or west as cir- 
cumstances permit. From such an observation the sun's hour- 
angle, i.e., the apparent solar time (Art. 422), is easily found, 
by a trigonometrical calculation, provided the ship's latitude 
is known. (For the method of calculation, see General As- 
tronomy, Art. 116.) 

The longitude follows at once, being simply the difference 
between the Greenwich time and the local time. 

In certain cases where the chronometers have been for 
some reason disturbed, the mariner is obliged to get his Green- 
wich time by observing with a sextant the distance of the 
moon from some neighboring fixed star, but the results thus 
obtained are comparatively inaccurate and unsatisfactory. 

428. To find the Form of the Earth's Orbit (supplementary 
to Art. 119). — Take the point 8 (Fig. 95) for the sun, and 



326 



APPENDIX. 



[§428 




draw from it a line, SO, directed toward the vernal equinox, 
from which longitudes are measured. Lay off from S lines 
indefinite in length, making angles with SO equal to the 

earth's longitude as seen 
from the sun on each 
of the days when the 
observations are made 
(earth's longitude equals 
sun's longitude + 180°). 
We shall thus get a sort 
of "spider," showing the 
direction of the earth as 
seen from the sun on 
each of those days. 

Next, as to the dis- 
tances. While the ap- 
parent diameter of the 
sun does not tell us its 
absolute distance from the earth, unless we know his diameter 
in miles, yet the changes in the apparent diameter do inform 
us as to the relative distance at different times, since the nearer 
we are to the sun, the larger it looks. If, then, on the legs of 
the " spider " we lay off distances inversely proportional l to the 
number of seconds of arc in the sun's measured diameter at 
each date, these distances will be proportional to the true dis- 
tance of the earth from the sun, and the curve joining the 
points thus obtained will be a true map of the earth's orbit, 
though without any scale of miles. When the operation is 
performed, we find that the orbit is an ellipse of small eccen- 
tricity, with the sun in one of the two foci. 

429. The Ellipse, and Definitions relating to it (supplemen- 
tary to Arts. 119, 120). — If we drive two pins into a board, as 
at F and S in Fig. 96, and put a looped thread around the 



Fig. 95. 
Determination of the Form of the Earth's Orbit. 



10000" 



> I.e., lay off Si, S 2 , etc., tach equal to diameter 



§ 429] DEFINITIONS RELATING TO THE ELLIPSE. 



327 





B 






/ / 


\ — ^>£ 




A 


/ ^ 


\\ 


\a 




F C 







pins, attached to the point of a pencil, P, then on carrying 

the pencil around it will mark out an ellipse. The pins, F 

and S, are the " foci " of the 

ellipse, and C is its centre. 

From the manner in which 

the ellipse is constructed, it 

is clear that at any point, P, 

on its outline, the sum of the 

two lines, PS and PF, will 

always be the same, and equal 

to the line AA\ The length 

of the ellipse, AA', is called Fm - ".-TheBiiip-e. 

its major axis, and AG its semi-major axis, which is usually 

designated by a, while the semi-minor axis, JBC, is lettered b. 

CS 
The fraction, -— , is called the eccentricity of the ellipse, and 

determines the shape of the oval. Its usual symbol is e. If e 
is nearly unity, — i.e., if CS is nearly equal to CA, — the oval 
will be very narrow compared with its length; but if CS is 
very small compared with CA, the ellipse will be almost round. 
Taken together, a and e determine the size and form of the 
oval. The ellipse is called a ' conic/ because when a cone is 
cut across obliquely the section is elliptical (see Art. 440). 

430. Problems illustrating the * Harmonic Law ' (supple- 
mentary to Art. 220). — To aid the student in apprehending the 
meaning and scope of Kepler's third law, we give a few simple exam- 
ples of its application. 

1. What would be the period of a planet having a mean distance 
from the sun of one hundred astronomical units ; i.e., a distance a 
hundred times that of the earth ? 

l 8 :100 3 =l 2 (year):X 2 ; 
whence, X (in years) = VlOO 8 = 1000 years. 

2. What would be the distance from the sun of a planet having a 
period of 125 years ? 

I 2 (year) : 125 2 - l 3 : X 8 ; whence X = \Zl25 2 = 25 astron. units. 



328 APPENDIX. [§ 430 

3. What would be the period of a satellite revolving close to the 
earth's surface ? 

(Moon's Dist.) 3 : (Disk of Satellite) 3 = (27.3 days) 2 : X\ 

or, 60 3 . p = 27.3 2 : X 2 ; 

whence, X = 27 _j^ days = 0^.587 = l h 24.5™. 
V60 3 

4. How much would an increase of 10 per cent in the earth's dis- 
tance from the sun lengthen the year? 

100 3 : 110 3 = (365}) 2 : X 2 , whence X =\ ;11 ° 8 x 86 °* 2 
v J V 100 3 

X being the new length of the year. X is found by logarithmic com- 
putation to be 421.38 days. The increase is 56.13 days. 

5. What is the distance from the sun of an asteroid with a period 
of 3 J years ? 

I 2 (year) : 3.5 2 = l 3 : Dist. 3 

.-. Dist. = \/(S^)" 2 = \/122h = 2.305 astron. units. 

431. The Equation of Light. — When we observe a celestial 
body, we see it not as it is at the moment of observation, but 
as it was at the moment when the light which we see left it. 
If we know its distance in astronomical units, and know how 
long light takes to traverse that unit, we can at once correct 
our observation by simply dating it back to the time when the 
light started from the object. The necessary correction is 
called the "equation of light" and the time required by light to 
traverse the astronomical unit of distance is called the "Con- 
stant of the Light-equation" (not quite 500 seconds, as 
we shall see). 

It was in 1675 that Roemer, the Danish astronomer (the inventor 
of the transit instrument, meridian-circle, and prime-vertical instru- 
ment, — a man almost a century in advance of his day), found that 
the eclipses of Jupiter's satellites show a peculiar variation in their 
times of occurrence, which he explained as due to the time taken by 
light to pass through space. His bold and original suggestion was 



§ 431] 



THE EQUATION OF LIGHT. 



329 



neglected for more than fifty years, until long after his death, when 
Bradley's discovery of aberration (Art. 435) proved the correctness of 
his views. 



432. Determination of the Constant of the Equation of 
Light. — Eclipses of the satellites of Jupiter recur at intervals 
which are really almost exactly equal (the perturbations being 
very slight) , and the interval can easily be determined and the 
times tabulated. But if we thus predict the times of the 
eclipses during a w^hole synodic period of the planet, then, be- 
ginning at the time of opposition, it is found that as the planet 
recedes from the earth, the eclipses, as observed, fall constantly 
more and more behindhand, and by precisely the same amount 
for all four satellites. The 
difference between the pre- 
dicted and observed time 
continues to increase until 
the planet is near conjunc- 
tion, when the eclipses are 
about 16 m 38 s later than the 
prediction. After the con- 
junction they quicken their 
pace, and make up the loss, 
so that when opposition is 
reached once more they are 
again on time. 

It is easy to see from 
Fig. 97 that at opposition 
the planet is nearer the earth than at conjunction by just two 
astronomical units. At opposition the distance between Jupi- 
ter and the earth is J A, while six and a half months later, 
at the time of Jupiter's superior conjunction, it is JB. The 
difference between J A and JB is just twice the distance from 
8 to A. 

The whole apparent Tetardation of eclipses between opposi- 




Fig. 97. — The Equation of Light. 



330 APPENDIX. L§ 432 

tion and conjunction must therefore be exactly twice the time l 
required for light to come from the sun to the earth. In this way 
the " light-equation constant " is found to be very nearly 499 
seconds, or 8 minutes 19 seconds, with a probable error of 
perhaps two seconds. 

433. Since these eclipses are gradual phenomena, the determination 
of the exact moment of a satellite's disappearance or reappearance is 
very difficult, and this renders the result somewhat uncertain. Prof. E. 
C. Pickering of Cambridge has proposed to utilize photometric observa- 
tions for the purpose of making the determination more precise, and 
two series of observations of this sort, and for this purpose, are now 
in progress, — one in Cambridge, United States, and the other at 
Paris under the direction of Cornu, who has devised a similar plan. 
Pickering has also applied photography to the observation of these 
eclipses with encouraging success. 

434. The Distance of the Sun determined by the "Light- 
equation." — Until 1849 our only knowledge of the velocity of 
light was obtained from such observations of Jupiter's satel- 
lites. By assuming as known the earth's distance from the sun, 
the velocity of light can be obtained when Ave know the time 
occupied by light in coming from the sun. 

At present, however, the case is reversed. We can deter- 
mine the velocity of light by two independent experimental 
methods, and with a surprising degree of accuracy. Then, 
knowing this velocity and the "light-equation constant," we 
can deduce the distance of the sun. According to the latest 
determinations the velocity of light is 186,330 miles per second. 
Multiplying this by 499 we get 92,979,000 miles for the sun's 
distance (compare Art. 436). 

1 The student's attention is specially directed to the point that the ob- 
servations of the eclipses of Jupiter's satellites give directly neither the 
velocity of light nor the distance of the sun : they give only the time re- 
quired by light to make the journey from the sun. Many elementary 
text- books, especially the older ones, state the case carelessly. 



435] 



ABERRATION OF LIGHT. 



331 



435. Aberration of Light. — The fact that light is not trans- 
mitted instantaneously causes the apparent displacement of 
an object viewed from any moving station, unless the motion 
is directly towards or from that object. If the motion of 
the observer is not rapid, this displacement, or " aberration," 
is insensible ; but the earth moves so swiftly (18^ miles 
per second) that it is easily observable in the case of the 
stars. Astronomical aberration may be defined, therefore, as 
the apparent displacement of a heavenly body due to the combina- 
tion of the orbital motion of the earth with that of light — the 
direction in which we have to point our telescope in observing 
a star is not the same as if the earth were at rest. 

We may illustrate this by considering what would happen in the 
case of falling rain-drops. Suppose the observer standing with a tube 
in his hand while the drops 
are falling straight down : if 
he wishes to have the drops 
descend through the middle of 
the tube without touching the 
sides, he must keep it vertical 
so long as he stands still ; but 
if he advances in any direction 
the drops will strike the side of 
the tube, and he must thrust 
forward its upper end (Fig. 98) 
by an amount which equals 
the advance he makes while a 
drop is falling through it ; i.e., 
he must incline the tube forward at an angle, depending both upon 
the velocity of the rain-drop and the swiftness of his own motion, 
so that when the drop, which entered the tube at B, reaches A 1 , the 
bottom of the tube will be there also. 

It is true that this illustration is not a demonstration, because light 
does not consist of particles coming towards us, but of waves trans- 
mitted through the ether of space. But it has been shown (though 
the proof is by no means elementary) that within very narrow limits, 
the apparent direction of a wave is affected in precisely the same way 
as that of a moving projectile. 




Fig. 98. — Aberration. 



332 APPENDIX. [§ 435 

The best observations show that a star situated on a line at 
right angles to the direction of the earth's motion, is thus 
apparently displaced by ah angle of about 20".5. The 
Pulkowa observations give 20".493, while, according to New- 
comb, the mean of all other determinations is 20".463. 
This is the so-called " Constant of Aberration." 
If the star i§ in a different part of the sky, its displacement 
will be less, the amount being easily calculated when the star's 
position is given. 

436. Determination of the Sun's Distance by Means of the 
Aberration of Light. — The constant of aberration, <x, and 
the two velocities, that of the earth in its orbit, u, and the 
velocity of light, V, are connected by the very simple equation 

a = 206265 X ^; whence u = — £— x V. 
V 206265 

When, therefore, we have ascertained the value of a (20 ".492) 
from observations of the stars, and of V (186,330 miles, ac- 
cording to the most recent determinations by Michelson and 
Newcomb) by physical experiments, we can immediately find 
u, the velocity of the earth in her orbit. The circumference of 
the earth's orbit is then found by multiplying this velocity, u, 
by the number of seconds in a sidereal year (Art. 127) ; and 
from this we get the radius of the orbit, or the earth's mean dis- 
tance from the sun, by dividing the circumference by 2?r (jr = 
3.14159). Taking a = 20".478, the mean distance of the sun 
comes out 92,913000 miles. 

But the uncertainty of a is probably as much as 0".03, and 
this affects the distance proportionally, say one part in 600, or 
150,000 miles. Still, the method is one of the very best of 
all that we possess for determining in miles the value of " the 
Astronomical Unit." 

437. De l'lsle's Method of determining the Sun's Parallax 
by a Transit of Venus. — We have thus (Arts. 434 and 436) 



§ 437] DETERMINING THE SUN'S PARALLAX. 333 

two methods by which the mean distance of the sun from the 
earth can be determined. They both depend upon a knowl- 
edge of the velocity of light, and of course were unavailable 
before 1849, when Fizeau first succeeded in actually measuring 
it. Before that time it was necessary to rely entirely upon 
observations of either Mars or Venus, made at times when 
they come specially near us. 

Most of the methods of getting the sun's parallax and dis- 
tance from such observations depend upon our having a pre- 
vious knowledge of the relative distances of the planets from 
the sun. These relative distances were ascertained centuries 
ago. Copernicus knew them nearly as accurately as we have 
them now; but since we have not explained in this book how 




Fig. 99. — Transit of Venus. 

they are found (the explanation involves a little Trigonom- 
etry), we limit ourselves to giving here a single very simple 
method, which requires a previous knowledge not of the rela- 
tive distances of Venus and the earth from the sun, but only 
of the synodic period of the planet (Art. 228); i.e., the time in 
which she gains one entire revolution . upon the earth. This 
is 584 days, as has been known from remote antiquity. 

Fig. 99 represents things at a transit of Venus, as they would 
be seen by one looking down from an infinitely distant point 
above the earth's north pole. As seen from the earth itself, 
Venus would appear to cross the sun, striking the disc on 
the east side and moving straight across to the west, mak- 
ing four ' contacts' with the edge of the sun as shown in 
Fig. 100. 







334 APPENDIX. [§ 438 

438. Suppose, now, that two observers, E and W (Fig. 99), 
are stationed opposite each other, and near the earth's equator. 

E will see Venus strike the sun's 
disc before W does, and if they 
both observe the moment of con- 
tact, in Greenwich time, the differ- 
ence between their records will be 
the time it takes Venus to move 
over the arc from Vi to V 2 - From 
the figure it is clear that the angle, 
ViDVa, is the same as EDW, the 
jtjo. 100 . earth's apparent diameter seen from 

Contacts in a Transit of Venus, the sun, and this is at once known 
when we have the time from V x to V 2 . 

Since Venus gains one revolution in 584 days, in one day 
she will gain z \^ of a revolution, or 37' (very nearly), and 
this will make her gain 1".54 in one minute. Now it is found 
that the difference between the moments of contact at two 
stations situated like E and W is about ll m 25 s , and hence that 
the diameter of the earth as seen from the sun is 17".6, or the 
sun's horizontal parallax (Art. 139) is 8".8 ; from which its 
distance is easily found (Art. 140). 

The reader will see that the two observers must know their 
longitudes accurately, in order to be sure of the correct Green- 
wich time. Moreover, the two stations can never be quite 
exactly opposite each other, but stations a little nearer together 
must be taken and proper allowances made. Finally, we are 
very sorry to add that the necessary observations of the mo- 
ment when Venus reaches the edge of the sun's disc cannot be 
made with the accuracy which is desirable, owing to the effect 
of the planet's atmosphere (see Art. 248) ; so that practically 
the method is less accurate than might be hoped. For fur- 
ther details, see General Astronomy, Chapter XVI. 

439. The Parabola (supplementary to Arts. 292-298). — This 
differs from the ellipse in never coming around into itself. 



§439] 



THE PAKABOLA. 



335 



In Fig. 101, the curves PA 1} PA 2 and PA 3 , are ellipses of dif- 
ferent length, all having S at one of their foci. The first and 
smallest of the ellipses is nearly circular, and shaped about 
like the orbit of Mercury ; the next, more eccentric than the 
orbit of any asteroid; and the third still more so. Now if we 




Fig. 101. —Ellipse, Parabola, and Hyperbola. 

imagine the point F carried farther and farther to the right, 
the ellipse will grow larger and longer, until when F is infi- 
nitely far away the curve will become a parabola. 

Of course if the point F is very distant, even if not infinitely 
so, the part of the curve near S will agree with the parabola 
so closely that no one could distinguish between them. 

All ellipses that have S for the focus and P for the perihe- 
lion lie inside of the parabola, while another set of conic curves 
called hyperbolas, with the same focus and perihelion, lie en- 
tirely outside of it, which is, so to speak, a sort of boundary 
or division line between the ellipses and hyperbolas which 
have this focus and perihelion. 



336 



APPENDIX. 



[§440 



440. The Conic Sections. — The way in which these curves, 
— the ellipse, parabola, and hyperbola — are formed by sec- 
tions of the cone is shown by Fig. 102. 

(a) If the cone be cut by a 
plane which makes with its 
axis, VC, an angle greater than 
BVC, the plane of the section 
will cut completely across the 
cone, and the section EF will 
be an ellipse, which will vary 
in shape and size according to 
the position of the plane. The 
circle is simply a special case 
when the cutting plane is per- 
pendicular to the axis, as NM. 

(b) When the cutting plane 
makes with the axis an angle 
less than B VC (the semi-angle 
of the cone), it plunges contin- 
ually deeper and deeper into 
the cone and never comes out 
on the other side (the cone is 
supposed to be indefinitely 
prolonged). The section in 
this case is an hyperbola, GHK. 
If the plane of the section be 
produced upward, however, it 
encounters the "cone pro- 
duced," cutting out from it 
a second hyperbola, G'lI'K', 
precisely like the original one, 

but turned in the opposite direction. 

The axis of the hyperbola is always reckoned as negative, 
lying outside of the curve itself: in the figure, it is the line 
HIT, The centre of the hyperbola is the middle point of this 
axis, a point also outside of the curve. 




Fig. 102.— The Conies. 



§440] STELLAR PARALLAX. 337 

(c) When the angle made by the' cutting plane with the 
axis is exactly equal to the cone's semi-angle, the plane will 
be parallel to the side of the cone, and we then get the special 
case of the parabola, RPO, which forms a partition, so to 
speak, between the infinite variety of ellipses and hyperbolas 
which can be cut from a given cone. All parabolas are of the 
same shape, just as all circles are, differing only in size. The 
fact is by no means self-evident, and we cannot stop to prove 
it, but it is true. 

441. Determination of the Parallax of a Star (supplemen- 
tary to Art. 343). — The determination of the parallax of stars 
had been attempted over and over again from the time of 
Tycho Brahe down, but without success until, in 1838, Bessel 
at last demonstrated and measured the parallax of 61 Cygni ; 
and the next year Henderson, of the Cape of Good Hope, 
determined that of Alpha Centauri. The operation of measur- 
ing the parallax of a star is on the whole the most delicate 
in the whole range of practical Astronomy. Two methods 
have been used so far, known as the absolute and the differential. 

442. The Absolute Method consists in making the most scru- 
pulously precise observations of the star's right ascension 
and declination with the meridian circle at different times 
through the course of an entire year, applying rigidly all 
known corrections (for precession, aberration, proper motion, 
etc.), and then examining the deduced positions. If the star 
is without parallax, these positions will all agree. If the star 
has a sensible parallax, they will show, on the other hand, 
when plotted on a chart, an apparent annual orbital motion of 
the star in a little ellipse, the major axis of which is twice the 
star's annual parallax, as can easily be shown. 

Theoretically, the method is perfect; practically, it seldom 
gives satisfactory results, because the annual changes of tem- 
perature and moisture disturb the instrument in such a way 



338 APPENDIX. [§ 442 

that the instrumental errors intertwine themselves with the 
parallax of a star in a manner that defies disentanglement. 
No process of multiplying observations and taking averages 
helps the matter very much, because the instrumental errors 
are themselves periodic annually, just as is the parallax; 
still, in a few cases the method has proved successful, as in 
the case of Alpha Centauri, above cited. 

443. The Differential Method. — This, the method which 
has principally proved successful thus far, consists in meas- 
uring the annual displacement of the star whose parallax we 
are seeking, with respect to other small stars near it in appar- 
ent position (i.e., within a few minutes of arc), but presuma- 
bly so far beyond as to have no sensible parallax of their own. 

If, for instance, the observer notes the apparent place of an 
object at no great distance from him with reference to the 
trees on a distant hill-side, and then moves a few feet one way 
or the other, he will see that the nearer object shifts its posi- 
tion with reference to the trees. In the same way, on account 
of the earth's orbital motion, those stars which are very near 
the earth appear every year to shift slightly backwards and 
forwards with respect to those that are far beyond them ; and 
by measuring the amount of this shift it is possible to deduce 
approximately the parallax and distance of the nearer stars. 

We say approximately, because the shift thus measured is 
not really the whole parallax of the nearer star, but only 
the difference between that parallax and the parallax of the 
remote objects with which it is compared; so that observa- 
tions, if accurately made, will always give us for the nearer 
star a parallax too small, if anything, — never too large; and, 
as a consequence, the distance of the nearer star determined 
in this way will come out a little too large, and never too small. 

444. The necessary measurements, if the comparison stars 
are within a minute or two of arc, may be made with the wire 



§ 444] STELLAR PARALLAX. 339 

micrometer (Art. 415) ; but if the distance exceeds a few min- 
utes, we must resort to the " heliometer " (see General Astron- 
omy, Art. 677), with which Bessel first succeeded ; or we may- 
employ photography, which Professor Pritchard at Oxford 
has recently been doing with remarkable success. 

On the whole, the differential method, notwithstanding the 
fundamental objection to it, that it never gives us the entire 
parallax of the star, is at present more trustworthy than the 
other. 

It is obviously necessary to choose for observation by either 
method those stars that are presumably near us. The most 
important indication of nearness in a star is a large proper 
motion ; brightness, also, is of course confirmatory. Still, 
neither of these indications is certain. A star which happens 
to be moving directly towards or from us shows no proper 
motion at all, however near it may be ; and the faint stars are 
so very much more numerous than the brighter ones that 
among their millions it is quite likely that we shall ultimately 
find individuals which are even nearer than Alpha Centauri. 

445. Spectroscopic Method. — In time it will be possible to 
determine the distance of certain binary stars by the help of 
the spectroscope. The velocity of one or both of the two 
stars " in the line of sight " can be measured by the spectro- 
scope at different parts of the star's orbit, and this will enable 
us to compute the size of the orbit in miles ; at the same time 
the micrometer measures will give its angular dimensions, 
and from these data the distance can be found. It will 
probably be many years, however, before any results can be 
obtained in this way, because the periods of most of the 
binaries are very long. 



340 APPENDIX. 



SUGGESTIVE QUESTIONS 



FOR USE IN REVIEWS. 



To many of these questions direct answers will not be 
found in the book; but the principles upon which the answers 
depend have been given, and the student will have to use his 
own thinking in order to make the proper application. 

1. What point in the celestial sphere has both its right ascension 
and declination zero ? 

2. What angle does the (celestial) equator make with the horizon 
at this place ? 

3. Name the (fourteen) principal points in the celestial sphere 
(zenith, etc.). 

4. What important circles in the heavens have no correlatives on 
the surface of the earth ? 

5. What constellation of the zodiac rises at sunset to-day, and 
which one is then on the meridian ? (Use the star-maps.) 

6. If Vega comes to the meridian at 8 o'clock to-night, at what 
time (approximately) will it transit eight days hence? 

7. What bright star can I observe on the meridian between 3 and 
4 p.m., in the middle of August? (See star-maps.) 

8. At what time of the year will Sirius be on the meridian at 
midnight? 

9. The declination of Vega is 38° 41'; does it pass the meridian 
north of your zenith, or south of it ? 

10. What are the right ascension and declination of the north pole 
of the ecliptic ? 

11. What are the longitude and latitude (celestial) of the north 
celestial pole (the one near the Pole-star) ? 



SUGGESTIVE QUESTIONS. 341 

12. Can the sun ever be directly overhead where you live? If not, 
why not ? 

13. What is the zenith distance of the sun at noon on June 22d in 
New York City (lat. 40° 42') ? 

14. What are the greatest and least angles made by the ecliptic 
with the horizon at New York ? Why does the angle vary ? 

15. If the obliquity of the ecliptic were 30°, how wide would the 
temperate zone be? How wide if the obliquity were 50°? What 
must the obliquity be to make the two temperate zones each as wide 
as the torrid zone? 

16. Does the equinox always occur on the same days of March and 
September? If not, why not; and how much can the date vary? 

17. Was the sun's declination at noon on March 10th, 1887, pre- 
cisely the same as on the same date in 1889 ? 

18. In what season of the year is New Year's Day in Chili? 

19. When the sun is in the constellation Taurus, in what sign of 
the zodiac is he ? 

20. In what constellation is the sun when he is vertically over the 
tropic of Cancer? Near what star? .(See star-map.) 

21. When are day and night most unequal? 

22. In what part of the earth are the days longest on March 20th? 
On June 20th ? On Dec. 20th ? 

23. Why is it warmest in the United States when the earth is 
farthest from the sun ? 

24. What will be the Russian date corresponding to Feb. 28th, 
1900, of our calendar ? To May 28th ? 

25. Why are the intervals from sunrise to noon and from noon to 
sunset usually unequal as given in the almanac ? (For example, see 
Feb. 20th and Nov. 20th.) 

26. If the earth were to shrink to half its present diameter, what 
would be its mean density? 

27. Is it absolutely necessary, as often stated, to know the diameter 
of the earth in order to find the distance of the sun from the earth? 

28. How will a projectile fired horizontally on the earth deviate 
from the line it would follow if the earth did not rotate on its axis ? 

29. If the earth were to contract in diameter, how would the weight 
of bodies on its surface be affected ? 

30. What keeps up the speed of the earth in its motion around the 
sun? 



342 APPENDIX. 

31. Why is the sidereal month shorter than the synodic? 

32. Does the moon rise every day of the month ? 

33. If the moon rises at 11.45 Tuesday night, when will it rise 
next ? 

34. How many times does the moon turn on its axis in a year ? 

35. What determines the direction of the horns of the moon ? 

36. Does the earth rise and set for an observer on the moon ? If so, 
at what intervals ? 

37. How do we know that the moon is not self-luminous? 

38. How do we know that there is no water on the moon ? 

39. How much information does the spectroscope give us about the 
moon ? 

40. What conditions must concur to produce a lunar eclipse ? 

41. Can an eclipse of the moon occur in the daytime ? 

42. Why can there not be an annular eclipse of the moon ? 

43. Which are most frequent at New York, solar eclipses or lunar? 

44. Can an occupation of Venus by the moon occur during a lunar 
eclipse? Would an occultation of Jupiter be possible under the same 
circumstances ? 

45. Which of the heavenly bodies are not self-luminous ? 

46. When is a planet an evening star ? 

47. What planets have synodic periods longer than their sidereal 
periods ? 

48. When a planet is at its least distance from the earth, what is 
its apparent motion in right ascension ? 

49. A planet is seen 120° distant from the sun ; is it an inferior or 
a superior planet ? 

50. Can there be a transit of Mars across the sun's disc? 

51. When Jupiter is visible in the evening, do the shadows of the 
satellites precede or follow the satellites themselves as they cross the 
planet's disc ? 

52. What would be the length of the month if the moon were four 
times as far away as now ? (Apply Kepler's third law.) 

53. What is the distance from the sun of an asteroid which has a 
period of eight years ? (Kepler's third law.) 

54. Upon what circumstances does the apparent length of a comet's 
tail depend ? 

55. How can the distance of a meteor from the observer, and its 
height above the earth, be determined ? 



SUGGESTIVE QUESTIONS. 343 

56. What heavenly bodies are not included in the solar system ? 

57. How do we know that stars are suns V How much is meant by 
the assertion that they are V 

58. Suppose that in attempting to measure the parallax of a bright 
star by the differential method (Art. 443) it should turn out that the 
small star taken as the point to measure from, and supposed to be far 
beyond the bright one, should really prove to be nearer. How would 
the measures show the fact? 

59. If Alpha Centauri were to travel straight towards the sun with 
a uniform velocity equal to that of the earth in its orbit, how long 
would the journey take, on the assumption that the star's parallax is 
0".75? 

60. If Altai r were ten times as distant from us, what would be its 
apparent " magnitude " ? What, if it were a thousand times as 
remote? (See Arts. 346, 347; and remember that the apparent 
brightness varies inversely with the square of the distance.) 



TABLES OF ASTRONOMICAL DATA. 



TABLES. 347 

TABLE I. — ASTRONOMICAL CONSTANTS. 

TIME CONSTANTS. 

The sidereal day = 23 h 56 m 4 8 .090 of mean solar time. 
The mean solar day = 24 h 3 m 56 8 .556 of sidereal time. 

To reduce a time interval expressed in units of mean solar 
time to units of sidereal time, multiply by 1.00273791; Log. of 
0.00273791= [7.4374191]. 

To reduce a time interval expressed in units of sidereal 
time to units of mean solar time, multiply by 0.99726957 = 
(1 - 0.00273043) ; Log. 0.00273043 = [7.4362316]. 

Tropical year (Leverrier, reduced to 1900), 365 d 5 h 48 m 45 8 .51. 
Sidereal year " « " 365 6 9 8.97. 

Anomalistic year " " " 365 6 13 48.09. 

Mean synodical month (new moon to new), 29 d 12 h 44 m 2 s . 684. 

Sidereal month, 27 7 43 11.545. 

Tropical month (equinox to equinox) , .27 7 43 4.68. 
Anomalistic month (perigee to perigee), . 27 13 18 37.44. 
Nodical month (node to node), . . 27 5 5 35.81. 



Obliquity of the ecliptic (Leverrier), 

23° 27' 08".0 - 0",4757 (t - 1900). 

Constant of precession (Struve), 

50".264 + 0".000227 (t -1900). 

Constant of nutation (Peters), 9".223. 

Constant of aberration (Nyren), 20".492. 



Equatorial semi-diameter of the earth (Clarke's spheroid of 
1880) , — 20 926 202 feet = 6 378 190 metre8 = 3963.296 mile8 . 

Polar semi-diameter, — 

20 854 895 feet = 6 356 456 metres = 3949.790 mUefl . 

Ellipticity, or Polar Compression, 29 3 >46 - 



348 



APPENDIX. 











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TABLES. 



349 



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5-2 








































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CO 


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350 



APPENDIX. 



TABLE IV. — THE PRINCIPAL VARIABLE STARS. 

A selection from S. C. Chandler's catalogue of variable stars, containing such as, 
at the maximum, are easily visible to the naked eye, have a range of variation 
exceeding half a magnitude, and can be seen in the United States. 





Name. 


Place, 1900. 


Range of 
Variation. 


Period (days). 


Remarks. 


o 


a 


8 




1 


R Andromeda 


h 



m 

18.8 


+ 38° 1* 


5.6 to 13 


411.2 


( Mira. Varia- 


2 


oCeti. . . . 


2 


14.3 


- 3 26 


1.7 


9.5 


331.3363 


J tions in length 
( of period. 
j Algol. Period 
) now shortening. 


3 


p Persei . . . 


2 


58.7 


+ 38 27 


3.4 


4.2 


33 


4 


/3 Persei . . . 


3 


1.6 


+ 40 34 


2.3 


3.5 


2d 20h 48» 55».43 


5 


ATauri . . . 


3 


55.1 


+ 12 12 


3.4 


4.2 


3d 22*» 52m 12s 


j Algol type, but 


6 


e Aurigas . . 


4 


54.8 


+ 43 41 


3 


4.5 


Irregular 


\ irregular. 


7 


a Orionis . . 


5 


49.7 


+ 7 23 


1 


1.6 


196 ? 


Irregular. 


8 


tj Geminorum . 


6 


8.8 


+ 22 32 


3.2 


4.2 


229.1 




9 


£ Geminorum . 


6 


58.2 


+ 20 43 


3.7 


4.5 


10d 3h 41m 30s 




10 


R Canis Maj. . 


7 


14.9 


-16 12 


5.9 


6.7 


Id 3 h 15™ 55^ 


Algol type. 


11 


R Leonis . . 


9 


42.2 


+ 11 54 


5.2 


10 


312.87 




12 


U Hydras . . 


10 


32.6 


-12 52 


4.5 


6.3 


194.65 




13 


R Hydras . . 


13 


24.2 


-22 46 


3.5 


9.7 


496.91 


Period short'ing 


14 


5 Libra? . . . 


14 


55.6 


- 8 7 


5.0 


6.2 


2d 7 h 51= 22s. 8 


Algol type. 


15 


R Coronas . . 


15 


44.4 


+ 28 28 


5.8 


13 


Irregular 




16 


R Serpentis . 


15 


46.1 


+ 15 26 


5.6 


13 


357.6 




17 


a Herculi* . . 


17 


10.1 


+ 14 30 


3.1 


3.9 


Two or three mon 


ths, but very irreg. 


18 


U Ophiuchi . 


17 


11.5 


+ 1 19 


6.0 


6.7 


20b 7m 41s.6 




19 


X Sagittarii . 


17 


41.3 


-27 48 


4 


6 


7.01185 




20 


W Sagittarii . 


17 


58.6 


-29 35 


5 


6.5 


7.59445 




21 


R Scuti . . . 


18 


42.1 


- 5 49 


4.7 


9 


71.10 


( Secondary mini- 
j mum about mid- 


22 


jS Lyras . . . 


18 


46.4 


+ 33 15 


3.4 


4.5 


12d 21 h 46* 58 3 .3 


23 
24 


x Cygni. . . 
tj Aquilas . . 


19 
19 


46.7 
47.4 


+ 32 40 
+ 45 


4.0 
3.5 


13.5 

4.7 


406.045 
7d 4b 14m os.0 


( way. 
Period length'ng 


25 


S Sagittas . . 


19 


51.4 


+ 16 22 


5.6 


6.4 


gd 9b llm 




26 


T Vulpeculas . 


20 


47.2 


+ 27 52 


5.5 


6.5 


4 d 10 h 29 m 




27 


T Cephei . . 


21 


8.2 


+ 68 5 


5.6 


9.9 


383.20 




28 


/a Cephei . . 


21 


40.4 


+ 58 19 


4 


5 


432 ? 




29 


8 Cephei . . 


22 


25.4 


+ 57 54 


3.7 


4.9 


5d gb 47 m 39\97 




30 


/3 Pegasi . . . 


22 


58.9 


+ 27 32 


2.2 


2.7 


Irregular 




31 


R Cassiopeia) . 


23 


53.3 


+ 50 50 


4.8 


12 


429.00 





TABLES. 



351 



TABLE V. — STELLAR PARALLAXES AND PROPER MOTIONS. 
(From Oudeman's Table, Ast. Nach., Aug., 18S9.) 



No. 


Name. 


Mag. 


Proper Motion. 


Annual 
Parallax. 


Distance' 
Light Years. 


1 


a Centauri 


0.7 


3".67 


0".75 


4 


2 


LI. 21185 


. . 6.9 


4.75 


0.50 


6.5 


3 


61 Cygni . 


5.1 


5.16 


0.40 


8 


4 


Sirius . 


. . -1.4 


1.31 


0.39 


8.3 


5 


2 2398 . 


. . 8.2 


2.40 


0.35 


9.3 


6 


LI. 9352 


7.5 


6.96 


0.28 


12 


7 


Procyon 


. . 0.5 


1.25 


0.27 


12.3 


8 


LI. 21258 


. . 8.5 


4.40 


0.26 


12.5 


9 


Altair . 


1.0 


0.65 


0.20 


16.3 


10 


« Indi . 


. . 5.2 


4.60 


0.20 


16.3 


11 


o 2 Eridani 


. 4.5 


4.05 


0.19 


17 


12 


Vega . . 


0.2 


0.36 


0.16 


20 


13 


/3 Cassiopc 


;ise, 2.4 


0.55 


0.16 


20 


14 


70 Ophiuc 


hi . 4.1 


1.13 


0.15 


21 


15 


e Eridani 


. . 4.4 


3.03 


0.14 


23 


16 


Aldebaran 


1.0 


0.19 


0.12 


27 


17 


Capella 


0.2 


0.43 


0.11 


29 


18 


Regulus 


1.4 


0.27 


0.10 


32 


19 


Polaris 


2.1 


0.05 


0.07 


47 



These are not all the stars upon Oudeman's list which are given as hav- 
ing parallaxes exceeding O'M ; but they are probably the best determined 
ones. A parallax of 0".45 is assigned to Eta Cassiopeia^ by a recent 
determination by Davis. 



THE GKEEK ALPHABET. 



Letters. Name. 


Letters. 


Name. 


Letters. 


Name. 


A, a, Alpha. 


I, I, 


Iota. 


Pj p> ^ 


Eho. 


B ; fl, Beta. 


K,K, 


Kappa. 


2, <T, S, 


Sigma. 


r, y, Gamma. 


A,\, 


Lambda. 


T,r, 


Tau. 


A, 8, Delta. 


M, /*, 


Mu. 


Y,v, 


Upsilon. 


E, c, Epsilon. 


N,n 


Nu. 


*> & 


Phi. 


Z, £ Zeta. 


ft 6 


Xi. 


x > X> 


Chi. 


H ; rj, Eta. 


0,0, 


Omicron. 


%k 


Psi. 


© ; 0, fl, Theta. 


II, 7T, za 


,pl 


O, <o, 


Omega. 


MISCELLANEOUS SYMBOLS. 




6 f Conjunction. 




A.E., or a, 


Eight Ascension. 


O, Quadrature. 




Peel., or 8, 


Declination. 


8> Opposition. 




A, Longitude (Celestial). 


Q,, Ascending Node 




/?, Latitude 


(Celestial). 


f3 f Descending Node. 


<£, Latitude 


, (Terrestrial). 



<o, Angle between line of nodes and line of apsides ; also 
the obliquity of the ecliptic. 



352 



INDEX, 



I N DKX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



A. 

Aberration, of light, 435 ; determining 
distance of sun, 436. 

Absolute scale of star magnitudes, 346. 

Acceleration of rotation at the sun's 
equator, 163. 

Achromatic telescope, 406, 407. 

Adams, J. C. (and Leverrier), dis- 
covery of Neptune, 283; orbit of the 
Leonids, 327. 

Aerolite. See Meteorite. 

Age of the sun and planetary system, 
193, 397-399. 

Albedo defined, 149, 235; of the moon 
(Zollner), 149 \ of the planets (Zoll- 
ner), 242, 247, 253, 268, 276, 281, 285. 

Algol, or 3 Persei, 40, 351, 368, 360. 

Alphabet, the Greek, page 344. 

Altitude defined, 11 ; parallels of, 11 ; 
of the pole equals latitude, 80. 

Andromeda, constellation of, 35; neb- 
ula of, 377, 378, 392, note; nebula of, 
temporary star in, 355. 

Andromedes, or Bielids, 312, 326. 

Angular measurements, units of, 8. 

Annual or heliocentric parallax de- 
fined, 343; methods of determining 
it for the stars by observation, 441- 
444. 

Annular eclipses, 201. 

Anomalistic year, 127. 

Anomalous phenomena in comets, 308. 

Apex of the sun's way, 342. 

Aphelion defined, 120. 

Apogee defined, 137. 



Apparent motion of a planet, 225-229; 
motion of the sun, 115-117; solar 
time, 88. 

Apsides, line of, defined, 20, 137; of 
the moon's orbit, 137. 

Aquarius, 78, 118. 

Aquila, 71. 

Arcs of meridian, measurementof, 105, 
110. 

Areas, equal, law of, 121, 137, 220. 

Argo Navis, 51. 

Ariel, a satellite of Uranus, 282. 

Aries, first of, defined, 17; constella- 
tion of, 38, 118. 

Asteroids, or minor planets, 260-263. 

Astronomical constants, table of, page 
339; day, beginning of, 90; symbols, 
page 344 ; unit, — see Distance of the 
sun. 

Astronomy, utility of, 1. 

Atmosphere of the moon, 148 ; of Mars, 
253; of Mercury, 242; of Venus, 248. 

Attraction of gravitation, its law, 
220, 221. 

Auriga, 41. 

Axis of the earth, 13, 109; its per- 
manence, 109. 

Azimuth defined, 11. 



R. 

Bayer, his system of lettering the 
stars, 24. 

Beginning of the century (Ceres dis- 
covered), 260; of the day, 90, 98- 

BbSSSL, dark stars, 350, 360; first 
measures stellar parallax, 441, 444. 
:>,r>r> 

For Supplementary Index see page 366. 



356 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Bethlehem, the star of, 355. 

Biela's comet, 311, 312. 

Bielids, or Andromedes, 312, 324, 328. 

Binary stars, 368-371. 

Bissextile year, 129. 

Bode's law, 219. 

Bond, W. C, discovery cf the " gauze 
ring" of Saturn, 277; discovery of 
Hyperion, 280. 

Bootes, 59. 

Bredichin, his theory of comets' tails, 
307. 

Brightness of comets, 291 ; of meteors, 
318; of stars, and causes of differ- 
ence, 345-350. 

Brooks, his comets, 2C0, 299. 



Cesar, Julius, reformation of the 

calendar, 129. 
Calendar, the, 128-130. 
Calory, the, defined, 187. 
Camelopardus, 31. 
Canals of Mars, 256. 
Cancer, 52, 118. 
Canes Venatici, 58. 
Canis Major, 49. 
Canis Minor, 48. 
Capricornus, 73, 118. 
Capture theory of comets, 298. 
Cardinal points denned, 16. 
Carrington, discovery of the peculiar 

law of the sun's rotation, 163. 
Cassini, J. D., discovers division in 

Saturn's ring, 277. 
Cassiopeia, 28. 
Catalogues of stars, 335. 
Celestial globe described, 400, 401; 

sphere, infinite, 6. 
Centaurus, 62. 

Centrifugal force due to earth's rota- 
tion, 111. 
Cepheus, 29. 

Ceres, the first of the asteroids, 260. 
Cetus, 39. 
Chandler, S. C, identification of 

Lexell's comet, 299; his catalogue 

of variable stars, 361. 



Changes, gradual, in the brightness 
of stars, 353; on the surface of the 
moon, 155. 

Chemical constitution of the sun, 175, 
176. 

Chromosphere of the sun, 180, 194; 
and prominences made visible by the 
spectroscope, 182. 

Chronograph, the, 417. 

Chronometer, the, 417 ; longitude by, 
96, 427. 

Circle, meridian, the, 81, 99, 418. 

Circles, hour, defined, 15. 

Circumpolar stars, latitude by, 81. 

Civil day and astronomical day, 90. 

Classification of the planets, Hum- 
boldt, 217; of stellar spectra, Secchi, 
363 ; of variable stars, 352. 

Clock, the astronomical, 417; its rate 
and error, 92, 93, 417. 

Clusters of stars, 376. 

Columba, 45. 

Colures defined, 117. 

Coma Berenices, 57. 

Comet, Biela's, 311, 312; Donati's, 289; 
Encke's, 293, 311; Lexell-Brooks, 
299; Halley's, 293; of 1882, 313, 
314. 

Comets, anomalous phenomena shown 
by, 308; attendant companions, 314; 
brightness and visibility, 291; cap- 
ture theory of their origin, 298; cen- 
tral stripe in tail, 308; connection 
with meteors, 327-329; constitution 
of, 300; danger from, 310; density 
of, 303; designation and nomencla- 
ture, 290; dimensions of, 301 ; elliptic, 
293, 297 ; envelopes in head, 305; fam- 
ilies of, 297; formation of the tail, 
306; their light and spectra, 304; 
mass of, 302; nature of, 309; num- 
ber of, 289; orbits of, 292, 293; peri- 
odic, their origin, 297, 298; sheath 
of comet of 1882, 314; tails or trains, 
300, 306-308; visitors to the solar 
system, 296. 

Comet-groups, 294. 

Conic sections, the, 440. 

Conjunction defined, 132, 227. 



INDEX. 



357 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Constant, solar, denned and discussed, 

187. 
Constellations, the, 4, 333. (For de- 
tailed description, see Chap. II.) 
Constitution of comets, 300; of the 

sun, 194. 
Contraction of a comet nearing the 

sun, 301; of the sun, Helmholtz's 

theory, 192, 396, 397. 
Copernicus, rotation of the earth, 

106; his system, 230. 
Corona Borealis, 60. 
Corona, the solar, 183-185. 
Coronium, hypothetical element of the 

corona, 184. 
Correction or error of a timepiece, 92, 

427. 
Corvus, 55. 
Cosmogony, 389-396. 
Crater, 55. 
Cygnus, 68. 



Dark stars, 350, 360. 

Darwin, G. H., demonstrates that a 
meteoric swarm behaves like a gas- 
eous nebula, 394. 

Day, beginning of, 98 ; civil and astro- 
nomical, 90. 

Declination denned, 14; determina- 
tion of, 99, 100 ; parallels of, 14. 

Degrees of latitude, length of, 110. 

Deimos, a satellite of Mars, 258. 

De l'Isle, his method of observing a 
transit of Venus, 437, 438. 

Delphinus, 74. 

Density of comets, 303; of the earth, 
113; of the moon, 143; of the sun, 
161. 

Designation and nomenclature of 
comets, 290; and nomenclature of 
the stars, 24, 334 ; and nomenclature 
of variable stars, 361. 

Diameter of a planet, how determined, 
232. 

Difference of brightness in stars, its 
causes, 350. 

Diffraction, telescopic, 408. 

Diffraction grating, the, 171, note. 



Dione, a satellite of Saturn, 280. 

Disc, spurious, of a star, 408. 

Displacement of spectrum lines by 
motion in line of sight, 179, 341, 373. 

Distance of a body as depending on 
its parallax, 140; of the moon, 141; 
of the nebulae, 382; of the planets 
from the sun, Table II., page 340; of 
the stars, 343, 441^44; of the sun, 
by aberration of light, 436; of the 
sun, by the equation of light, 434; 
of the sun, by its parallax, 437. 

Distribution of the nebulae, 382; of 
the stars in the heavens, 384; of sun 
spots, 169. 

Diurnal or geocentric parallax defined, 
139 ; rotation of the heavens, 12. 

Doppler's principle, 179. 

Double stars, 366, 367; optical and 
physical, distinguished, 367. 

Draco, 30. 

Draper, H., photograph of the nebu- 
la of Orion, 378 ; photographs of star 
spectra, 364. 

Duration of solar eclipses, 203 ; prob- 
able, of the solar system, 193, 397- 
399. 

Earth, the, astronomical facts relating 
to it, 102; its density, 113; dimen- 
sions of, 105, 110, Table I.; ellip- 
ticity or oblateness determined, 110; 
its interior constitution, 114; mass, 
113; orbital motion of, 115-122, 428; 
its orbit, changes in, 122; its rota- 
tion, invariability of, 108; its rota- 
tion, proofs of, 107; shadow of, its 
dimensions, 196; surface area and 
volume, 112; velocity in its orbit, 
158. 

Earth-shine on the moon, 147. 

Ebb defined, 210. 

Eccentricity of the earth's orbit, 119; 
of an ellipse defined, 119, 429. 

Eclipses, frequency of, 206; of Jupi- 
ter's satellites, 273; lunar, 197-199; 
Oppolzer's canon of, 205; number in 
a year, 206; recurrence of, 207; so- 



358 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



lar, duration of, 203 ; solar, phenom- 
ena of, 204; solar, varieties of, total, 
annular, and partial, 201, 202. 

Ecliptic, the, denned, 116; obliquity 
of, 110; poles of, 117. 

Elements, chemical, recognized in the 
stars, 362; chemical, recognized in 
the sun, 176; of the planets' orbits, 
Table II., page 340. 

Ellipse, the, defined and described, 
429, 439, 440. 

Elliptic comets, 292, 293. 

Ellipticity, or oblateness of the earth, 
110. 

Elongation defined, 132, 227. 

Enceladus, a satellite of Saturn, 280. 

Encke's comet, 293, 311. 

Energy of the solar radiation, 188, 
189. 

Envelopes in the head of a comet, 305, 
314. 

Equation of light, 431-433 ; of time, 89. 

Equator, celestial or equinoctial, de- 
fined, 14. 

Equatorial acceleration of the sun's 
surface rotation, 163; instrument, 
the, 414; use in determining the 
place of a heavenly body, 100. 

Equinoctial, the, or celestial equator, 
defined, 14. 

Equinox, vernal, defined, 17, 116. 

Equinoxes, precession of, 125, 126. 

Equuleus, 75. 

Eridanus, 44. 

Error or correction of a timepiece, 92, 
93, 417. 

Eruptive prominences on the sun, 182. 

Establishment of a port, 210. 

Eye-pieces, telescopic, various forms, 
409. 



Facul33, solar, 165. 

Families of comets, 297. 

Faye, depth of sun spots, 168; modi- 
fication of the nebular hypothesis, 
393. 

Filar micrometer, the, 415. 

Flood tide, 210. 



Form of the earth's orbit determined, 

428. 
Foucault, his pendulum experiment, 

107. 
Fraunhofer lines in the solar spec 

trum, 175, note. 
Frequency of eclipses, 206. 

G. 

Galaxy, the, 383. 

Galileo, his discovery of Jupiter's 
satellites, 272; discovery of phases 
of Venus, 247 ; discovery of Saturn's 
ring, 277; discovery of sun spots, 
169; his telescope, 402. 

Gemination of the canals of Mars, 256. 

Gemini, 47, 118. 

Genesis of the planetary system, 390, 
391. 

Geocentric parallax, 139. 

Gibbous phase defined, 146. 

Globe, the celestial, described, 400, 401. 

Grating, diffraction, 171, note. 

Gravitation, 221, 222. 

Gravity, at the moon's surface, 143; 
at the pole and equator of the earth, 
111 ; at the sun's surface, 161; super- 
ficial, of a planet, how determined, 
233. 

Greek alphabet, the, page 344. 

Gregorian calendar, the, 130. 

Groups, cometary, 294. 

Grus, 79. 

Gyroscope illustrating the cause of the 
seasons, 123. 

H. 

Habitability of Mars, 259. 

Hall, A., discovery of the satellites of 
Mars, 258. 

Halley discovers the proper motion 
of stars, 339 ; his periodic comet, 293. 

Harmonic law, Kepler's, 220, 430. 

Harvest and hunter's moons, the, 136. 

Heat of meteors, its explanation, 318; 
from the moon, 150; from the stars, 
34S, note; of the sun, its constancy, 
191; of the sun, its intensity, 190; 
of the sun, its maintenance, 192; of 
the sun, its quantity, 187, 189. 



INDEX. 



359 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Heavenly bodies defined and enumer- 
ated, 2; apparent place of, 7. 

Heliocentric, or annual parallax, de- 
fined, 139, 343. 

Helium, hypothetical element in the 
sun, 181. 

Helmholtz, his theory of the sun's 
heat, 192. 

Hercules, 66. 

Herschel, Sir J., illustration of the 
solar system, 238; his names for the 
satellites of Saturn and Uranus, 280, 
282. 

Herschel, Sir W., discovery of Ura- 
nus, 281 ; his great telescope, 412 ; re- 
lation between nebulae and stars, 395. 

Herschels, the, their star-gauges, 
384. 

Hipparchus, 120, 125, 335, 345. 

Horizon defined, rational and visible, 
10. 

Horizontal parallax, 139. 

Hour-angle defined, 422. 

Hour-Circles defined, 15. 

Hourly number of meteors, 321. 

Huggins, W., observes spectrum of 
Mars, 253; observes spectrum of 
Mercury, 242; observes spectrum 
of nebulae, 380; observes spectrum 
of stars, 362; observes spectrum of 
temporary star of 1866, 355 ; spectro- 
scopic measures of star motions, 341. 

Humboldt, his classification of the 
planets, 217. 

Hunter's moon, the, 136. 

Huyghens, his discovery of Saturn's 
ring, 277; discovery of Titan, 280; 
invention of the pendulum clock, 
417. 

Hydra, 55. 

Hyperbola, the, 439, 440. 

Hyperion, a satellite of Saturn, 280. 



Iapetus, the remotest satellite of Sat- 
urn, 280. 

Identification of the orbits of certain 
comet« and meteors, 328. 



Illuminating power of a telescope, 

405. 
Illumination of the moon's disc dur- 
ing a lunar eclipse, 198. 
Illustration of the proportions of the 

solar system, 238. 
Influence of the moon on the earth, 

151 ; of sun spots on the earth, 170. 
Intensity of the sun's heat, 189-190; 

of the sun's light, 186. 
Intra- Mercurian planets, 264. 
Invariability of the earth's rotation, 

108; of the length of the year and 

distance from the sun, 122. 
Iron in comets, 314; in meteorites, 

316 ; in stars, 362 ; in the sun, 175. 



Julian calendar, the, 129. 

Juno, the third asteroid, 260. 

Jupiter (the planet), 266-271 ; his belts, 
red spot, and other markings, 268, 
271; his rotation, 270; his satellites 
and their eclipses, 272, 273. 

Jupiter's family of comets, 297. 



Kant, a proposer of the nebular hy- 
pothesis, 391. 

Kepler, his laws of planetary motion, 
121,220,430. 

Kirchhoff, fundamental principles of 
spectrum analysis, 173. 

Lacerta, 76. 

Langley, S. P., his value of the solar 
constant, 188. 

Laplace, his capture theory of comets, 
298 ; his nebular hypothesis, 392, 393; 
stability of the solar system, 288*. 

Lassell, his discovery of Ariel and 
Cmbriel, 282; his discovery of the 
satellite of Neptune, 286. 

Latitude (celestial) defined, 20; (ter- 
restrial) defined, 80; length of de- 
grees, 110 ; methods of determining, 
81, 424,426; variations of, 109. 

Law, Bode's, 219 ; of the earth's orbital 
motion, 121 ; of gravitation, 221, 222. 



360 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Laws, Kepler's, 121, 220, 430. 

Leap-year, 129, 130. 

Leo, 53, 118. 

Leo minor, 54. 

Leonids, the, 324, 325, 326, 329. 

Lepus, 45. 

Leverrier (and Adams), discovery 
of Neptune, 283; on the origin of the 
Leonids, 329. 

Libra, 61, 118. 

Librations of the moon, 145. 

Lick telescope, the, 412. 

Light, aberration of, 435, 436; of com- 
ets, 291; equation of, the, 432, 433; 
of the moon, 149 ; of the sun, its in- 
tensity, 186; of the stars, 348-350; 
velocity of, used to determine the 
distance of the sun, 434, 436; the 
zodiacal, 265. 

Light-ratio of the scale of stellar mag- 
nitude, 346. 

Light-year, the, 344. 

Local time, 97 ; time from altitude of 
the sun, 427 ; time by transit instru- 
ment, 93, 416. 

Lockyer, J. N., his meteoritic hypothe- 
sis, 330, 394; on spectra of nebulas, 
380. 

Longitude and latitude (celestial) 20 ; 
(terrestrial), defined, 94; (terres- 
trial), methods of determining it, 
95, 96, 427. 

Lunar. See Moon. 

Lupus, 62. 

Lynx, 46. 

Lyra, 67. 

Magnesium in nebulae (Lockyer), 380; 
in the stars, 362 ; in the sun, 176. 

Magnifying power of a telescope, 404. 

Magnitudes, star, 345-347; star, abso- 
lute scale of, 346; star, and tele- 
scopic power, 347. 

Mars (the planet), 251-257; habita- 
bility of, 259; map of the planet, 
257; satellites, 258; Schiaparelli's 
observations, etc., 256; telescopic 
aspect, rotation, etc., 253, 254. 



Mass, definition, 113 ; of comets, 302 ; 
of earth, 113; of the moon, 143; of a 
planet, how determined, 233; of 
shooting stars, how estimated, 323; 
of the sun, 161. 

Masses of binary stars, 371. 

Mazapil, meteorite of, 326. 

Mean and apparent places of stars, 
336 ; and apparent solar time, 88-89. 

Melbourne reflector, 412. 

Mercury (the planet), 239-244; rota- 
tion of, 243 ; transits of, 244. 

Meridian (celestial) defined, 11, 15, 16 ; 
(terrestrial), arcs of, measured, 105, 
110; circle, the, 81, 99, 418. 

Meteoritic hypothesis (Lockyer), 330, 
394; showers, 324-326. 

Meteorite of Mazapil, 326. 

Meteorites, 315; their constituents, 
316; their fall, 315. 

Meteors, ashes of, 323; connection 
with comets, 327-329 ; heat and light, 
318; observation of, 317; origin of, 
319 ; path and velocity, 317. 

Micrometer, the, 415. 

Midnight sun, the, 86. 

Milky Way, the, 383. 

Mimas, the inner satellite of Saturn, 
280. 

Mir a Ceti, 356. 

Missing and new stars, 353. 

Monoceros, 50. 

Month, sidereal and synodic, 133. 

Moon, its albedo, 149 ; its atmosphere 
discussed, 148; changes on its sur- 
face, 155; character of its surface, 
153; density, 143; diameter, surface 
area and bulk, 142; distance and 
parallax, 141 ; eclipses of, 195-199; 
heat, 150; influence on the earth, 
151; librations, 145; light and albedo, 
149; map, 154, 156; mass, density, and 
gravity, 143; motion (in general), 
132-135 ; nomenclature of objects on 
surface, 156; perturbations of, 134; 
phases, 146; rotation, 144; shadow 
of, 200 ; surface structure, 153 ; tele- 
scopic appearance, 152; tempera- 
ture, 150 ; water not present, 148. 



INDEX. 



361 



[All references, unless expressly stated to the contraiy, are to articles, not to pages.] 



Motion, apparent diurnal, of the 
heavens, 12, 13; of the moon, 132-134; 
of a planet, 225, 226, 229 ; of the sun, 
115-117; in line of vision, effect on 
spectrum, 179, 341; of the sun in 
space, 342. 

Motions of stars, 338-341. 

Mountains, lunar, 153, 156. 

Mounting of a telescope, 414. 

Multiple stars, 375. 

Nadir defined, 10. 

Nadir-point of meridian circle, 419. 

Names of planets, 218 ; of satellites of 
Saturn, 280 ; of satellites of Uranus, 
282. 

Neap tide, 210. 

Nebulae, the, 377-382; changes in, 379; 
distance and distribution, 382 ; spec- 
tra of, 380, 381. 

Nebular hypothesis, the, 392, 393. 

Negative eye-pieces, 409. 

Neptune (the planet), 283-287. 

Newcomb, S., on the age and duration 
of the system, 193; and Michelson, 
the velocity of light, 436. 

Newton, H. A., estimate of the daily 
number of meteors, 321 ; investiga- 
tion of the orbit of the Leonids, 327 ; 
nature of comets, 309. 

Newton, Sir Isaac, law of gravita- 
tion, 221, 222. 

Nodes of the moon's orbit and their 
regression, 134; of the planetary 
orbits, 224. 

Nordenskiold, ashes of meteors, 323. 

Norma, 64. 

Number of comets, 289 ; of eclipses in 
a saros, 207; of eclipses in a year, 
206 ; of the stars, 332. 

Nyren, his value of the aberration 
constant, 435. 

O. 

Oberon, a satellite of Uranus, 282. 

Oblateness or ellipticity of the earth 
denned, 110. 

Oblique sphere, 85. 

Obliquity of the ecliptic, 116. 



Olbers, discovers Pallas and Vesta, 
260. 

Ophiuchus, 65. 

Oppolzer, his canon of eclipses, 205. 

Opposition denned, 132, 227. 

Orbit of the earth, its form, etc., 115, 
122, 428 ; of the moon, 137 ; parallac- 
tic, of a star, 442. 

Orbital motion of the earth, proof of 
it, 115. 

Orbits of binary stars, 370 ; of comets, 
292 ; of the planets, 223. 

Origin of the asteroids, 263 ; of mete- 
ors, 319; of periodic comets, 297. 

Orion, 43. 

I». 

Palisa, discovery of asteroids, 260. 
Pallas, the second asteroid, 260. 
Parabola, the, 439, 440. 
Parallax, annual or heliocentric, of 

the stars, 139, 343, 441-441; diurnal 

or geocentric, 139 ; solar, by transit 

of Venus, de l'Isle's method, 437; 

stellar, how determined, 441-444. 
Parallaxes, stellar, table of, Table V., 

page 343. 
Parallel sphere, 84. 
Pegasus, 77. 
Pendulum used to determine earth's 

form, 111; Foucault, 107. 
Perigee denned, 137. 
Perihelion denned, 120. 
Periodicity of sun spots, 169. 
Periods of the Planets, 218; sidereal 

and synodic, 133, 162, 228. 
Perseids, the, 324-326, 328, 329. 
Perseus, 40. 
Perturbations, lunar, 134; planetary, 

122, 288*. 
Peters, asteroid discoveries, 260. 
Phase of Mars, 253. 
Phases of Mercury and Venus, 242, 

247 ; of the moon, 146 ; of Saturn's 

rings, 278. 
Phobos, a satellite of Mars, 258. 
Phoenix, 39. 
Photographic power of eclipsed moon, 

198; star-charts, 337; telescopes, 337. 



362 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Photographs of nebulae, 378 ; of star- 
spectra, 341, 364. 

Photography, solar, 164. 

Photometry, stellar, 348, 349. 

Photosphere, the, 165, 194. 

Piazzi discovers Ceres, 260. 

Pickering, E. C, photographs of star- 
spectra, 364, 373 ; photometric obser- 
vations of eclipses of Jupiter's satel- 
lites, 433; photometric measures of 
stellar magnitudes, 346. 

Pisces, 36, 118. 

Piscis Australis, 79. 

Place of a heavenly body defined, 7; 
of a heavenly body, how determined 
by observation, 99, 100; of a ship, 
how determined, 426, 427. 

Planet, albedo of, denned, 231, 235; 
apparent motion of, 225-229 ; diame- 
ter and volume, how measured, 232 ; 
mass and density, how determined, 
233; rotation on axis determined, 
234; satellite system, how investi- 
gated, 236 ; superficial gravity deter- 
mined, 233. 

Planetary data, their relative accu- 
racy, 237; system, its genesis, age, 
and duration, 390-398 ; its stability, 
288*. 

Planetoids. See Asteroids. 

Planets, Humboldt's classification, 
217; the list of, 218; intra-Mercurian, 
264; minor, 260-263 ; possibly attend- 
ing stars, 372; table of elements, 
Appendix, Table II., page 340; table 
of names, symbols, etc., 218. 

Pleiades, the, 42, 376. 

Pointers, the, 12, 26. 

Pole (celestial), altitude of, equals 
latitude, 80; defined, 13; effect of 
precession, 126; (terrestrial), diur- 
nal phenomena near it, 83. 

Pole-star, former, a Draconis, 126; 
how recognized, 12. 

Positive eye-pieces, 409. 

Precession of the equinoxes, 125, 126. 

Prime vertical, the, 11. 

Proctor, sun spots, 168; theory of 
comets, 298. 



Prominences, the solar, 181, 182, 194 
Proper motion of stars, 339. 
Ptolemaic system, the, 230. 
Ptolemy, 4, 230. 



Quadrature defined, 132, 227. 
Quiescent prominences, 182. 

R. 

Radiant, the, of a meteoric shower 
324. 

Radius vector defined, 120. 

Rate of a timepiece defined, 417- 

Rectification of a globe, 401. 

Recurrence of eclipses, 207. 

Red spot of Jupiter, 271. 

Reflecting telescope, the, 411, 413. 

Refracting telescope, the, 403-407, 413. 

Refraction, astronomical, 82. 

Reticle, the, 410, 416. 

Retrograde and retrogression defined, 
226. 

Reversing layer, 177. 

Rhea, a satellite of Saturn, 280. 

Right ascension defined, 18, 93; how 
determined by observation, 99, 100. 

Right sphere, the, 83. 

Rings of Saturn, the, 277-279. 

Roberts, photographs of nebulae, 378. 

Rosse, Lord, his great reflector, 412. 

Rotation, apparent diurnal, of the 
heavens, 12; definition of, 144; dis- 
tinguished from revolution, 106, note ; 
of earth, its effect on gravity, 111; 
of earth, proofs of, 107; of earth, 
variability of, 108; of the moon, 144; 
of the sun, 162, 163. 

Rotation-period of Jupiter, 270; of 
Mars, 254; of Mercury, 243; of a 
planet, how ascertained, 234; of 
Saturn, 275; of Venus, 249. 



Sagitta. 70. 
Sagittarius, 72, 118. 
Saros, the, 207. 



INDEX. 



363 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Satellite system, how investigated, 
236; systems, table of, Table 111., 
page 341. 

Satellites of Jupiter, 272; of Mars, 
258; of Neptune, 286; of Saturn, 
280; of Uranus, 282. 

Saturn (the planet), 274-280. 

Scale of stellar magnitudes, 346. 

Schiaparellt, identification of come- 
tary and meteoric orbits, 328 ; obser- 
vations of Mars, 256; rotation of 
Mercury and Venus, 243, 249. 

Schwabe, discovers periodicity of sun 
spots, 169. 

Scintillation of the stars, 365. 

Scorpio, 63, 118. 

Sea, position at, how found, 426, 427. 

Seasons, explanation of, 123-124. 

Secchi, on stellar spectra, 363; on 
sun spots, 168. 

Secondary spectrum of achromatic 
object-glass, 407. 

Serpens, 65. 

Serpentarius, 65. 

Sextant, the, 420, 421. 

Shadow of the earth, its dimensions, 
196; of the moon, its dimensions, 
200; of the moon, its velocity, 203. 

Ship at sea, determination of its posi- 
tion, 426, 427. 

Shooting stars (see also Meteors) 320- 
324; ashes of, 323; brightness of, 
323; elevation and path, 322; mass 
of, 323; materials of, 323; nature of, 
320; number, daily and hourly, 321; 
radiant, 324; showers of, 324-326; 
spectrum of, 323 ; velocity of, 322. 

Showers, meteoric, 324-326. 

Sidereal and synodic months, 133 ; and 
synodic periods of planets, 228 ; time 
defined, 91; year, 127. 

Signs of the zodiac, 118; effect of pre- 
cession on them, 126. 

Sirius, its companion, 369; light com- 
pared with that of the sun, 349; its 
mass compared with that of the sun, 
370. 

Solar constant, the, 187; parallax, 158 ; 
time, mean and apparent, 88, 89. 



Solstice defined, 117. 

Sosigenes and the calendar, 129. 

Spectroscope, its principle and con- 
struction, 171, 172; slitless, 364, 445; 
used to observe the solar promi- 
nences, 182 ; used to measure motions 
in line of sight, 178, 179, 341, 373, 
374. 

Spectrum of the chromosphere and 
prominences, 181 ; of comets in gen- 
eral, 304; of the comet of 1882, 314; 
of meteors, 323; of nebulae, 380, 
381 ; of a shooting star, 323 ; of 
stars, 362-364; the solar, 172-175; of 
the solar corona, 184; of a sun spot, 
178. 

Spectrum analysis, fundamental prin- 
ciples, 173. 

Speculum of a reflecting telescope, 
411. 

Sphere, celestial, the, 6; doctrine of 
the, 9-20. 

Spots, solar. See Sun spots. 

Spring tide defined, 210. 

Stability of the planetary system, 288*. 

Standard time, 97. 

Stars, binary, 368-371; catalogues of, 
335; charts of, 337; clusters of, 376; 
dark, 350,360; designation and no- 
menclature, 24, 334; dimensions of, 
351, 360; distance of, 343, 344; distri- 
bution of, 384; double, 366, 367; 
gravitation among them, 368, 371, 
386 ; heat from them, 348, note ; light 
of certain stars compared with sun- 
light, 348, 349; magnitudes and 
brightness, 345-350; mean and ap- 
parent places of, 336; missing and 
new, 353; motions of, 338-342; mul- 
tiple, 375; new, 353; number of, 
332 ; parallax of, 343, 441-444 ; Table 
V., page 343; shooting (see Shoot- 
ing stars, also Meteors) ; spectra of, 
362-364; system of the, 386; tem- 
porary, 355; total amount of light 
from the, 348; twinkling of, 365; 
variable, 352-361 ; Table IV., page 
342. 

Star- gauges of the Herschels, 384. 



364 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Starlight, its total amount, 348. 

Stellar parallaxes, table of, Table V., 
page 343 ; photometry, 348, 349. 

Structure of the stellar universe, 385. 

Sun, the age and duration of, 193, 397, 
398 ; apparent motion in the heavens, 
115-117; its chromosphere, 180; its 
constitution, 194; its corona, 183- 
185 ; its density, 161 ; dimensions of, 
160; distance of, 158, 159, 434-438; 
elements recognized in it, i76; fac- 
ulse, 165 ; gravity on its surface, 161 ; 
heat of, quantity, intensity and 
maintenance, 187-192; light of, its 
intensity, 186 ; mass of, 161 ; motion 
in space, 342; parallax of, 159; 
prominences, 181, 182, 194; revers- 
ing layer, the, 177, 194 ; rotation of, 
162, 163 ; spectrum of, 172, 175 ; tem- 
perature of, 190 ; temperature dimin- 
ishing, Lockyer, 396, note. 

Sun spots, appearance and nature, 166, 
170; cause of, 168; distribution of, 
169; influence on the earth, 170; 
periodicity of, 169 ; spectrum of, 178. 

Superficial gravity of a planet, how 
determined, 233. 

Surface structure of the moon, 153, 
154. 

Swarms, meteoric, 324-329. 

Synodic and sidereal months, 133 ; and 
sidereal periods of planets, 228. 

System, planetary, its age and dura- 
tion, 397-399; its genesis and evo- 
lution, 390-393; its stability, 288*; 
stellar, its probable nature, 386-388. 

Syzygy defined, 132. 

T 

Tables, astronomical constants, Table 
I., page 339; astronomical symbols, 
page 344; binary stars, orbits and 
masses, 370; Bode's law, 219; con- 
stellations, showing place in heavens, 
page 54 ; Greek alphabet, page 344 ; 
moon, names of principal objects, 
155; planet's elements, Table II., 
page 340; planets' names, distances, 



etc., approximate, 218; satellite sys- 
tems, Table III., page 341; stellar 
parallaxes and proper motions, Table 
V., page 343; variable stars, Table 
IV., page 342. 

Tails of comets, 300, 301, 305-308. 

Taurus, 42. 

Telegraph, longitude by, 95. 

Telescope, achromatic, 406, 407; eye- 
pieces of, 409 ; general principles of, 
402; illuminating power, 405; mag- 
nifying power, 404; magnitude of 
stars visible with a given aperture, 
347; mounting of, 414; reflecting,' 
411 ; simple refracting, 403. 

Telescopes, great, 412. 

Temperature of the moon, 150; of the 
sun, 190. 

Temporary stars, 355. 

Terminator, the, defined and described, 
146. 

Tethys, a satellite of Saturn, 280. 

Thomson, Sir W., the internal heat of 
the earth, 396; the heat of meteors, 
318 ; the rigidity of the earth, 114. 

Tidal-wave, course of, 213. 

Tides, the definitions relating to, 210 
due mainly to moon's action, 209 
explanation of, 208, 209, 211, 212 
height of, 214 ; motion of, 211, 213 : in 
rivers, 215. 

Time, equation of, 89 ; local, from sun's 
altitude, 427; methods of determin- 
ing, 92, 93, 427; relation to hour- 
angle, 422; sidereal, defined, 91; 
solar — mean and apparent, 88, 89 ; 
standard, defined, 97. 

Titan, satellite of Saturn, 280. 

Titania, satellite of Uranus, 282. 

Total and annular eclipses, 201. 

Trains of meteors, 315. 

Transit or meridian circle, 81, 99, 418. 

Transit instrument, the, 92, 416. 

Transits of Mercury, 244; of Venus, 
250. 

Triangulum, 37. 

Tropical year, the, 127. 

Twinkling of the stars, 365. 

Tycho Brahe, his temporary star, 355, 



INDEX. 



365 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 

Volcanoes on the moon, 153. 

Vulcan, the hypothetical intra-Mercu- 

rian planet, 264. 
Vulpecula, 69. 



u. 

Ultra-Neptunian planet, 288. 
Umbriel, a satellite of Uranus, 282. 
Universe, stellar, its structure, 385. 
Uranography defined, 5. 
Uranolith, or Uranolite. See Meteor- 
ite. 
Uranus (the planet), 281, 282. 
Ursa Major, 26. 
Ursa Minor, 27. 
Utility of astronomy, 1. 



Vanishing point, 6, note. 

Variable stars, 352-361; table of, 
Table IV., page 342. 

Velocity of earth in its orbit, 102, 158 ; 
of light, 436; of moon's shadow, 
203; of meteors and shooting stars, 
317, 322 ; of star motions, 340, 341. 

Venus (the planet),. 245-250; phases 
of, 247 ; transits of, 250. 

Vernal equinox, the, 17, 36, 116. 

Vertical circles, 11. 

Vesta, the fourth asteroid, 260. 

Virgo, 56, 118. 

Visible horizon defined, 10. 

Vogel, H. C, spectroscopic determina- 
tion of star motions in the line of 
sight, 341; spectroscopic observa- 
tions of Algol and Spica, 3G0, 374. 



W. 

Water absent from the moon, 148. 
Wave-length of a light-ray affected 

by motion in the line of sight, Dop- 

pler's principle, 179, 341. 
Wave, tidal, its course, 213. 
Way, the sun's, 342. 
Weather, the moon's influence on, 151. 
Weight, loss of, between pole and 

equator, 111. 



Year, the sidereal, tropical, and anom- 
alistic, 127, and Table I., page 339. 

Z. 

Zenith, the, defined, 10. 
Zenith distance defined, 11. 
Zero-points of the meridian circle, 418, 

419. 
Zodiac, the, and its signs, 118 ; its signs 

as affected by precession, 126. 
Zodiacal light, the, 265. 
Zollner, determination of planets' 

albedoes, 242, 247, 253, 268, 276, 281, 

285 ; measurement of moonlight, 149; 

measures of light of stars, 348. 



SUPPLEMENTARY INDEX. 



[All references are to articles.] 



Barnard, E. E. , measures of diameters 
of planets, 262, 267, 275, 285; dis- 
covery of the fifth satellite of Jupi- 
ter, 272 ; of comets, 314.* 

Boys, V., determination of density of 
the earth, 113. 

Calcium, in the sun, 176; in faculae, 
165; in chromosphere and promi- 
nences, 182, 182.* 

Campbell, W. C, spectrum of Mars, 
253 ; of nebulae, 380. 

Chandler, S. C, variation of latitude, 
109. 

Charlois, discoverer of asteroids by 
photography, 260. 

Chromosphere, photography of, 182.* 

Deslandres, photography of solar 
prominences, 182.* 

Faculse, bright lines of calcium in spec- 
trum, 165. 

H and K lines of calcium, 165, 176, 182, 

182.* 
Hale, G. E., photography of solar 

prominences, 182.* 
Helium, identification of, in uraninite, 

181 ; in variable stars, 355, 356 ; in 

nebulae, 380. 

Keeler, J. E., spectroscopic observa- 
tion of the rings of Saturn, 279 ; of 
nebulae, 380. 



Kelvin, Lord (formerly Sir Wm. 
Thomson), 114, 318, 396. 

Lick Observatory, telescope, 412 ; vari- 
ous observations, 156, 253, 256, 262, 
267, 272, 275, 299, 314*, 380. 

Lowell, P., observations on Mars, 
256. 

Oases, on Mars, 256. 

Parallax, stellar, determination of, by 
spectroscopic observations on binary 
stars, 445. 

Photography, of solar prominences, 
182* ; applied to discovery of aster- 
oids, 260 ; of comets, 314.* 

Pole (terrestrial), motion and displace- 
ment of, 109. 

Ramsay, Prof., identifies Helium, 181. 

See, T. J. J., evolution of binary stars, 
370. 

Spoerer, peculiar law of sun-spot lati- 
tude, 169. 

Struve, H., mass of Saturn's rings, 
277. 

Wilson and Gray, temperature of 
the sun, '190. 

Wolf, photographic discovery of aster- 
oids, 260. 



Yerkes telescope, 412. 



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